Nondeterministic hybrid dynamical systems

This thesis is concerned with the analysis, control and identification of hybrid dynamical systems. The main focus is on a particular class of hybrid systems consisting of linear subsystems. The discrete dynamic, i.e., the change between subsystems, is unknown or nondeterministic and cannot be influenced, i.e. controlled, directly. However changes in the discrete dynamic can be detected immediately, such that the current dynamic (subsystem) is known. In order to motivate the study of hybrid systems and show the merits of hybrid control theory, an example is given. It is shown that real world systems like Anti Locking Brakes (ABS) are naturally modelled by such a class of linear hybrids systems. It is shown that purely continuous feedback is not suitable since it cannot achieve maximum braking performance. A hybrid control strategy, which overcomes this problem, is presented. For this class of linear hybrid system with unknown discrete dynamic, a framework for robust control is established. The analysis methodology developed gives a robustness radius such that the stability under parameter variations can be analysed. The controller synthesis procedure is illustrated in a practical example where the control for an active suspension of a car is designed. Optimal control for this class of hybrid system is introduced. It is shows how a control law is obtained which minimises a quadratic performance index. The synthesis procedure is stated in terms of a convex optimisation problem using linear matrix inequalities (LMI). The solution of the LMI not only returns the controller but also the performance bound. Since the proposed controller structures require knowledge of the continuous state, an observer design is proposed. It is shown that the estimation error converges quadratically while minimising the covariance of the estimation error. This is similar to the Kalman filter for discrete or continuous time systems. Further, we show that the synthesis of the observer can be cast into an LMI, which conveniently solves the synthesis problem

Contributions à la stabilisation des systèmes à commutation affine

Cette thèse porte sur la stabilisation des systèmes à commutation dont la commande, le signal de commutation, est échantillonné de manière périodique. Les difficultés liées à cette classe de systèmes non linéaires sont d'abord dues au fait que l'action de contrôle est effectuée aux instants de calcul en sélectionnant le mode de commutation à activer et, ensuite, au problème de fournir une caractérisation précise de l'ensemble vers lequel convergent les solutions du système, c'est-à-dire l'attracteur. Dans cette thèse, les contributions ont pour fil conducteur la réduction du conservatisme fait pendant la définition d'attracteurs, ce qui a mené à garantir la stabilisation du système à un cycle limite. Après une introduction générale où sont présentés le contexte et les principaux résultats de la littérature, le premier chapitre contributif introduit une nouvelle méthode basée sur une nouvelle classe de fonctions de Lyapunov contrôlées qui fournit une caractérisation plus précise des ensembles invariants pour les systèmes en boucle fermée. La contribution présentée comme un problème d'optimisation non convexe et faisant référence à une condition de Lyapunov-Metzler apparaît comme un résultat préliminaire et une étape clé pour les chapitres à suivre. La deuxième partie traite de la stabilisation des systèmes affines commutés vers des cycles limites. Après avoir présenté quelques préliminaires sur les cycles limites hybrides et les notions dérivées telles que les cycles au Chapitre 3, les lois de commutation stabilisantes sont introduites dans le Chapitre 4. Une approche par fonctions de Lyapunov contrôlées et une stratégie de min-switching sont utilisées pour garantir que les solutions du système nominal en boucle fermée convergent vers un cycle limite. Les conditions du théorème sont exprimées en termes d'Inégalités Matricielles Linéaires (dont l'abréviation anglaise est LMI) simples, dont les conditions nécessaires sous-jacentes relâchent les conditions habituelles dans cette littérature. Cette méthode est étendue au cas des systèmes incertains dans le Chapitre 5, pour lesquels la notion de cycles limites doit être adaptée. Enfin, le cas des systèmes dynamiques hybrides est exploré au Chapitre 6 et les attracteurs ne sont plus caractérisés par des régions éventuellement disjointes mais par des trajectoires fermées et isolées en temps continu. Tout au long de la thèse, les résultats théoriques sont évalués sur des exemples académiques et démontrent le potentiel de la méthode par rapport à la littérature récente sur le sujet.This thesis deals with the stabilization of switched affine systems with a periodic sampled-data switching control. The particularities of this class of nonlinear systems are first related to the fact that the control action is performed at the computation times by selecting the switching mode to be activated and, second, to the problem of providing an accurate characterization of the set where the solutions to the system converge to, i.e. the attractors. The contributions reported in this thesis have as common thread to reduce the conservatism made in the characterization of attractors, leading to guarantee the stabilization of the system at a limit cycle. After a brief introduction presenting the context and some main results, the first contributive chapter introduced a new method based on a new class of control Lyapunov functions that provides a more accurate characterization of the invariant set for a closed-loop system. The contribution presented as a nonconvex optimization problem and referring to a Lyapunov-Metzler condition appears to be a preliminary result and the milestone of the forthcoming chapters. The second part deals with the stabilization of switched affine systems to limit cycles. After presenting some preliminaries on hybrid limit cycles and derived notions such as cycles in Chapter 3, stabilizing switching control laws are developed in Chapter 4. A control Lyapunov approach and a min-switching strategy are used to guarantee that the solutions to a nominal closed-loop system converge to a limit cycle. The conditions of the theorem are expressed in terms of simple linear matrix inequalities (LMI), whose underlying necessary conditions relax the usual one in this literature. This method is then extended to the case of uncertain systems in Chapter 5, for which the notion of limit cycle needs to be adapted. Finally, the hybrid dynamical system framework is explored in Chapter 6 and the attractors are no longer characterized by possibly disjoint regions but as continuous-time closed and isolated trajectory. All along the dissertation, the theoretical results are evaluated on academic examples and demonstrate the potential of the method over the recent literature on this subject

Vehicle dynamics virtual sensing and advanced motion control for highly skilled autonomous vehicles

This dissertation is aimed at elucidating the path towards the development of a future generation of highly-skilled autonomous vehicles (HSAV). In brief, it is envisaged that future HSAVs will be able to exhibit advanced driving skills to maintain the vehicle within stable limits in spite of the driving conditions (limits of handling) or environmental adversities (e.g. low manoeuvrability surfaces). Current research lines on intelligent systems indicate that such advanced driving behaviour may be realised by means of expert systems capable of monitoring the current vehicle states, learning the road friction conditions, and adapting their behaviour depending on the identified situation. Such adaptation skills are often exhibited by professional motorsport drivers, who fine-tune their driving behaviour depending on the road geometry or tyre-friction characteristics. On this basis, expert systems incorporating advanced driving functions inspired by the techniques seen on highly-skilled drivers (e.g. high body slip control) are proposed to extend the operating region of autonomous vehicles and achieve high-level automation (e.g. manoeuvrability enhancement on low-adherence surfaces). Specifically, two major research topics are covered in detail in this dissertation to conceive these expert systems: vehicle dynamics virtual sensing and advanced motion control. With regards to the former, a comprehensive research is undertaken to propose virtual sensors able to estimate the vehicle planar motion states and learn the road friction characteristics from readily available measurements. In what concerns motion control, systems to mimic advanced driving skills and achieve robust path-following ability are pursued. An optimal coordinated action of different chassis subsystems (e.g. steering and individual torque control) is sought by the adoption of a centralised multi-actuated system framework. The virtual sensors developed in this work are validated experimentally with the Vehicle-Based Objective Tyre Testing (VBOTT) research testbed of JAGUAR LAND ROVER and the advanced motion control functions with the Multi-Actuated Ground Vehicle “DevBot” of ARRIVAL and ROBORACE.Diese Dissertation soll den Weg zur Entwicklung einer zukünftigen Generation hochqualifizierter autonomer Fahrzeuge (HSAV) aufzeigen. Kurz gesagt, es ist beabsichtigt, dass zukünftige HSAVs fortgeschrittene Fahrfähigkeiten aufweisen können, um das Fahrzeug trotz der Fahrbedingungen (Grenzen des Fahrverhaltens) oder Umgebungsbedingungen (z. B. Oberflächen mit geringer Manövrierfähigkeit) in stabilen Grenzen zu halten. Aktuelle Forschungslinien zu intelligenten Systemen weisen darauf hin, dass ein solches fortschrittliches Fahrverhalten mit Hilfe von Expertensystemen realisiert werden kann, die in der Lage sind, die aktuellen Fahrzeugzustände zu überwachen, die Straßenreibungsbedingungen kennenzulernen und ihr Verhalten in Abhängigkeit von der ermittelten Situation anzupassen. Solche Anpassungsfähigkeiten werden häufig von professionellen Motorsportfahrern gezeigt, die ihr Fahrverhalten in Abhängigkeit von der Straßengeometrie oder den Reifenreibungsmerkmalen abstimmen. Auf dieser Grundlage werden Expertensysteme mit fortschrittlichen Fahrfunktionen vorgeschlagen, die auf den Techniken hochqualifizierter Fahrer basieren (z. B. hohe Schlupfregelung), um den Betriebsbereich autonomer Fahrzeuge zu erweitern und eine Automatisierung auf hohem Niveau zu erreichen (z. B. Verbesserung der Manövrierfähigkeit auf niedrigem Niveau) -haftende Oberflächen). Um diese Expertensysteme zu konzipieren, werden zwei große Forschungsthemen in dieser Dissertation ausführlich behandelt: Fahrdynamik-virtuelle Wahrnehmung und fortschrittliche Bewegungssteuerung. In Bezug auf erstere wird eine umfassende Forschung durchgeführt, um virtuelle Sensoren vorzuschlagen, die in der Lage sind, die Bewegungszustände der Fahrzeugebenen abzuschätzen und die Straßenreibungseigenschaften aus leicht verfügbaren Messungen kennenzulernen. In Bezug auf die Bewegungssteuerung werden Systeme zur Nachahmung fortgeschrittener Fahrfähigkeiten und zum Erzielen einer robusten Wegfolgefähigkeit angestrebt. Eine optimale koordinierte Wirkung verschiedener Fahrgestellsubsysteme (z. B. Lenkung und individuelle Drehmomentsteuerung) wird durch die Annahme eines zentralisierten, mehrfach betätigten Systemrahmens angestrebt. Die in dieser Arbeit entwickelten virtuellen Sensoren wurden experimentell mit dem Vehicle-Based Objective Tyre Testing (VBOTT) - Prüfstand von JAGUAR LAND ROVER und den fortschrittlichen Bewegungssteuerungsfunktionen mit dem mehrfach betätigten Bodenfahrzeug ”DevBot” von ARRIVAL und ROBORACE validiert

Heterogeneous and hybrid control with application in automotive systems

Control systems for automotive systems have acquired a new level of complexity. To fulfill the requirements of the controller specifications new technologies are needed. In many cases high performance and robust control cannot be provided by a simple conventional controller anymore. In this case hybrid combinations of local controllers, gain scheduled controllers and global stabilisation concepts are necessary. A considerable number of state-of-the-art automotive controllers (anti-lock brake system (ABS), electronic stabilising program (ESP)) already incorporate heterogeneous and hybrid control concepts as ad-hoc solutions. In this work a heterogeneous/hybrid control system is developed for a test vehicle in order to solve a clearly specified and relevant automotive control problem. The control system will be evaluated against a state-of-the-art conventional controller to clearly show the benefits and advantages arising from the novel approach. A multiple model-based observer/estimator for the estimation of parameters is developed to reset the parameter estimate in a conventional Lyapunov based nonlinear adaptive controller. The advantage of combining both approaches is that the performance of the controller with respect to disturbances can be improved considerably because a reduced controller gain will increase the robustness of the approach with respect to noise and unmodelled dynamics. Several alternative resetting criteria are developed based on a control Lyapunov function, such that resetting guarantees a decrease in the Lyapunov function. Since ABS systems have to operate on different possibly fast changing road surfaces the application of hybrid methodologies is apparent. Four different model based wheel slip controllers will be presented: two nonlinear approaches combined with parameter resetting, a simple linear controller that has been designed using the technique of simultaneously stabilising a set of linear plants as well as a sub-optimal linear quadratic (LQ)-controller. All wheel slip controllers operate as low level controllers in a modular structure that has been developed for the ABS problem. The controllers will be applied to a real Mercedes E-class passenger car. The vehicle is equipped with a brake-by-wire system and electromechanical brake actuators. Extensive real life tests show the benefits of the hybrid approaches in a fast changing environment

Stability analysis and controller design for switched time-delay systems

In this thesis, the stability analysis and control synthesis for uncertain switched time-delay systems are investigated. It is known that a wide variety of real-world systems are subject to uncertainty and also time-delay in their dynamics. These characteristics, if not taken into consideration in analysis and synthesis, can lead to important problems such as performance degradation or instability in a control system. On the other hand, the switching phenomenon often appears in numerous applications, where abrupt change is inevitable in the system model. Switching behavior in this type of systems can be triggered either by time, or by the state of the system. A theoretical framework to study various features of switched systems in the presence of uncertainty and time-delay (both neutral and retarded) would be of particular interest in important applications such as network control systems, power systems and communication networks. To address the problem of robust stability for the class of uncertain switched systems with unknown time-varying delay discussed above, sufficient conditions in the form of linear matrix inequalities (LMI) are derived. An adaptive switching control algorithm is then proposed for the stabilization of uncertain discrete time-delay systems subject to disturbance. It is assumed that the discrete time-delay system is highly uncertain, such that a single fixed controller cannot stabilize it effectively. Sufficient conditions are provided subsequently for the stability of switched time-delay systems with polytopic-type uncertainties. Moreover, an adaptive control scheme is provided to stabilize the uncertain neutral time-delay systems when the upper bounds on the system uncertainties are not available a priori . Simulations are provided throughout the thesis to support the theoretical result

Contributions to Control of Electronic Power Converters

This thesis deals with the control of electronic power converters. In its development two main parts have been differentiated. On the one hand, the problem of the voltage balance in the capacitors of the dc-link in a three-level NPC converter is addressed. On the other hand, given that the techniques used in the first part to model the converters need to make certain assumptions and, with the intention of avoiding averaged models, in the second part, switched affine models have been developed to design the control of the output voltage in DC-DC boost type converters. In this way, in the first part several control laws have been developed using an averaged model formulated by duty cycles for each level in each phase. This formulation allows to consider, in the controllers design stage, the degree of freedom associated with the homopolar voltage injection. Therefore, the controllers are designed as well as a part of the modulation, so that control and modulation are integrated in the same stage. In this way, three controllers have been designed where, apart from the objective of the voltage balance of the capacitors, other objectives such as the number of commutations or the quality of the output signal have also been improved. In the second part of the thesis, four methods have been developed for the design of control laws taking advantage of the modeling of converters as switched affine systems given their hybrid behaviour. Thus, the first two laws take advantage of this modeling using the delta operator to avoid numerical problems when using systems where the sampling time is very low. The first of these controllers is based on Lyapunov’s function while the second is independent of this function, thus obtaining less conservative results. The other two laws developed for switched affine systems use an alternative model to that performed in the first two controllers, so certain existing disadvantages are avoided using again a design not based on Lyapunov’s function. Thus, the first law presents a basic control but, even so, improves the results of other existing laws in the literature. Finally, a design method to deal with systems with variations in their parameters has been presented.La presente tesis trata sobre el control de convertidores electrónicos de potencia. En su desarrollo se han diferenciado dos partes principales. Por un lado, se trata el problema del balance de tensiones en los condensadores que forman el dc-link en un convertidor NPC de tres niveles. Por otro lado, dado que las técnicas utilizadas en la primera parte para modelar los convertidores necesitan realizar determinadas suposiciones y, con la intención de evitar modelos promediados, en la segunda parte se han desarrollado modelos afines conmutados para diseñar el control de la tensión de salida en convertidores DC-DC tipo boost. De esta forma, en la primera parte se han desarrollado varias leyes de control utilizando un modelo promediado formulado mediante ciclos de trabajo para cada nivel en cada fase. Esta formulación permite considerar en la fase de diseño de los controladores, un grado de libertad asociado a la inyección de tensión homopolar. Por lo tanto, se diseñan los controladores a la vez que una parte de la modulación, de forma que se integra control y modulación en una misma fase. De esta forma, se han diseñado tres controladores donde, a parte del objetivo de balancear la tensión de los condensadores, se ha ido buscando mejorar también otros objetivos como el número de conmutaciones o la calidad de la señal de salida. En la segunda parte de la tesis, se han desarrollado cuatro leyes de control aprovechando el modelado de convertidores como sistemas afines conmutados dada su naturaleza híbrida. De esta forma, las dos primeras leyes, aprovechan dicho modelado usando el operador delta para evitar problemas numéricos al utilizar sistemas donde el tiempo de muestreo es muy bajo. El primero de dichos controladores está basado en la función de Lyapunov mientras que el segundo es independiente de dicha función obteniendo así resultados menos conservadores. Las otras dos leyes desarrolladas para sistemas afines conmutados utilizan un modelado alternativo al realizado en las dos primeras, de forma que se evitan ciertas desventajas existentes y mantienen un diseño no basado en la función de Lyapunov. Así, la primera ley presenta un control más básico pero que, aun así, mejora los resultados de otras leyes existentes en la literatura. Por último, se ha presentado un procedimiento de diseño que hace frente a sistemas con variaciones en sus parámetros

Air Traffic Control

Improving air traffic control and air traffic management is currently one of the top priorities of the global research and development agenda. Massive, multi-billion euro programs like SESAR (Single European Sky ATM Research) in Europe and NextGen (Next Generation Air Transportation System) in the United States are on their way to create an air transportation system that meets the demands of the future. Air traffic control is a multi-disciplinary field that attracts the attention of many researchers, ranging from pure mathematicians to human factors specialists, and even in the legal and financial domains the optimization and control of air transport is extensively studied. This book, by no means intended to be a basic, formal introduction to the field, for which other textbooks are available, includes nine chapters that demonstrate the multi-disciplinary character of the air traffic control domain

Delay-dependent output feedback compensators for a class of networked control systems

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2014Sistemas de controle via rede (NCS, do inglês Networked Control Systems) são uma classe especial de sistemas amostrados digitalmente, nos quais os dispositivos do sistema de controle se comunicam através de uma rede de comunicação (como mostrado na Fig. I). Significantes avanços tecnológicos tem levado a um maior interesse tanto na utilização de NCS em ambiente industrial (MOYNE; TILBURY, 2007), quanto em pesquisas relacionadas ao assunto (HESPANHA; NAGHSHTABRIZI; XU,2007; HEEMELS; WOUW, 2010; ZHANG; GAO; KAYNAK, 2013). Algumas das vantagens oferecidas por tais sistemas, com relação a sistemas de controle tradicionais, compreendem menor custo de implementação, flexibilidade e facilidade de manutenção. Apesar disso, inerentemente alguns efeitos indesejados também podem ocorrer, tais como atrasos na comunicação e intervalos de amostragem variantes, ocasionando degradação no desempenho do sistema em malha fechada. Devido a esses efeitos, a análise de estabilidade e também o projeto de controladores para NCS tornam-se mais desafiadores (TANG; YU, 2007). De modo geral, os estudos sobre NCS podem ser divididos em duas grandes áreas: controle da rede e controle via rede (GUPTA; CHOW, 2010). A primeira está mais interessada em proporcionar uma melhor qualidade no serviço de transmissão de dados realizado pela rede de comunicação, enquanto a segunda objetiva uma melhor qualidade do desempenho dos sistemas de controle sob determinadas condições induzidas pelos efeitos da utilização da rede. Embora tipicamente tratadas de forma separada, recentemente alguns esforços têm sido empreendidos de modo a integrar algumas características de ambas as áreas em fase de projeto, as chamadas estratégias de co-design (TORNGREN et al., 2006). Uma abordagem integrada é necessária de modo a se obter uma maior compreensão do funcionamento de um NCS, podendo assim obter um melhor desempenho geral do sistema. Neste contexto, especialmente levando em consideração que o uso rede de comunicação é limitado, tal recurso deve ser corretamente distribuído entre os sistemas de controle de modo a garantir um funcionamento adequado. Além disso, requisitos de desempenho individuais de cada planta também devem ser cumpridos, mesmo sujeitos a tais restrições de limites de recursos.Abstract: Networked control system (NCS) is a special class of sampled-data system where control systems devices are interconnected through a communication network. Despite the advantages, such as lower cost, flexibility and easy of maintenance compared to a more traditional implementation, some undesired effects may be induced by the use of a shared medium in the feedback loop, for instance, time-varying sampling intervals and delays. Due to the multidisciplinary nature of an NCS, the analysis and design of such systems also demand a more comprehensive approach. Thus, the main objective of this thesis is to propose some strategies for the synthesis of dynamic output feedback compensators, assuming an industrial network control system environment with temporal behavior features and requirements. Throughout this document, the NCS is modeled considering unknown time-varying delays, which leads to an uncertain system representation, later overapproximated by a convex polytope with additional norm-bounded uncertainty. Based on parameter dependent Lyapunov functions, closed-loop stability conditions are provided, which can be verified in terms of feasibility of a set of linear matrix inequalities (LMIs). The control designs are then promptly derived from the stability conditions, leading to delay-dependent compensators. Furthermore, an integrated control design and resource management strategy is proposed, taking into account the controller design while also addressing the shared nature of the communication network. This co-design strategy assumes that a supervisor task has the knowledge of all devices that access the network, as well as their allocated bandwidths. Numerical examples and simulations are provided to illustrate the effectiveness of the proposed design methodologies

Stability Analysis and Design of Digital Compensators for Networked Control Systems

Networked Control Systems (NCSs) are distributed control systems where sensors, actuators, and controllers are interconnected by communication networks, e.g. LAN, WAN, CAN, Internet. Use of digital networks are advantageous due to less cost, ease in installation and/or ready availability. These are widely used in automobiles, manufacturing plants, aircrafts, spacecrafts, robotics and smart grids. Due to the involvement of network in such systems, the closed-loop system performance may degrade due to network delays and packet losses. Since delays are involved in NCS, predictor based compensators are useful to improve control performance of such systems. Moreover, the digital communication network demands implementation of digital compensators. First, the thesis studies stability analysis of NCSs with uncertain time-varying delays. For this configuration, both the controller and actuators are assumed as event-driven (i.e. the delays are fractional type). The NCS with uncertain delays and packet losses are represented as systems in polytopic form as well as with norm-bounded uncertainties. The closed-loop system stability is guaranteed using quadratic Lyapunov function in terms of LMIs. For given controller gain the maximum tolerable delay calculated and the resultant stability regions of the system is explored in the parameter plane of control gain and maximum tolerable delay. The stability region is found to be almost same for both the methods for the case of lower order systems (an integrator plant), whereas for higher order systems (second order example system), the obtained stability region is more for the case of polytopic approach than the norm-bounded one. This motivates to use the polytopic modeling approach in remaining of the thesis. Next, design of digital Smith Predictor (SP) to improve the performance of NCS with bounded uncertain delays and packet losses in both the forward and feedback channels is con-sidered. For implementing a digital SP, it is essential that the controller is implemented with constant sampling interval so that predictor model is certain and therefore the controller is required to be time-driven one (sensor-to-controller channel uncertainties are integer type). On the other hand, the actuator is considered to be event-driven since it introduces lesser delay compared to the time-driven case. Thereby, the controller-to-actuator channel delays are fractional type. The system with uncertain delay parameters (packet losses as uncertain integer delays) are modeled in polytopic form. For this system, Lyapunov stability criterion has been presented in terms of LMIs to explore the closed-loop system stability. Finally, the proposed analysis is verified with numerical studies and using TrueTime simulation en- vironment. It is observed that the digital SP improves the stability performance of the NCS considerably compared to without predictor. However, the choice of predictor delay affects the system performance considerably. Further, an additional filter is used along with conventional digital SP to improve the system response and disturbance rejection property of the controller. For this configurations, both the controller and actuators are assumed to be time-driven. The NCS with random but bounded delays and packet losses introduced by the network is modeled as a switched system and LMI based iterative algorithm is used for designing the controller. A LAN-based experimental setup is developed to validate the above theoretical findings.The plant is an op-amp based emulated integrator plant.The plant is interfaced with a computer using data acquisition card. Another computer is used as the digital controller and the two computers are connected via LAN using UDP communication protocol. The effectiveness of the proposed controller design method is verified with this LAN-based experi- mental setup. Three controller configurations (i.e. without and with digital SP as well as the digital SP with filter) are considered for comparison of their guaranteed cost performance. It is shown that the digital SP with filter improves the performance of NCS than with and without simple digital SP based NCS configurations. Finally, design of digital predictor based robust H1 control for NCSs is made in such a way that the effect of randomness in network delays and packet losses on the closed-loop system dynamics is reduced. For the purpose, the predictor delay is chosen as a fixed one whereas variation of random delays in the system are modeled as disturbances. Then quadratic H1 design criterion in the form of LMIs is invoked so that the network jitter effect is minimized. The efficacy of the proposed configurations are validated with the developed LAN based NCS setup. It is seen that the designed controllers effectively regularize the system dynamics from random variations of the network delays and packet losses