New H∞ control design for polytopic systems with mixed time-varying delays in state and input

This paper concerns with the problem of state-feedback H∞ control design for a class of linear systems with polytopic uncertainties and mixed time-varying delays in state and input. Our approach can be described as follows. We first construct a state-feedback controller based on the idea of parameter-dependent controller design. By constructing a new parameter-dependent Lyapunov-Krasovskii functional (LKF), we then derive new delay-dependent conditions in terms of linear matrix inequalities ensuring the exponential stability of the corresponding closed-loop system with a H∞ disturbance attenuation level. The effectiveness and applicability of the obtained results are demonstrated by practical examples

Finite-Time Stabilization of Uncertain Switched Positive Linear Systems with Time-Varying Delays

This paper is concerned with finite-time stabilization (FTS) analysis for a class of uncertain switched positive linear systems with time-varying delays. First, a new definition of finite-time boundedness (FTB) is introduced for switched positive system. This definition can simplify FTS analysis. Taking interval and polytopic uncertainties into account, a robust state feedback controller is built such that the switched positive linear system is finite-time bounded. Finally, an example is employed to illustrate the validities of obtained results

Stability Results for Switched Linear Systems with Constant Discrete Delays

Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/543145This paper investigates the stability properties of switched systems possessing several parameterizations (or configurations) while being subject to internal constant point delays. Some of the stability results are formulated based on Gronwall's lemma for global exponential stability, and they are either dependent on or independent of the delay size but they depend on the switching law through the requirement of a minimum residence time. Another set of results concerned with the weaker property of global asymptotic stability is also obtained as being independent of the switching law, but still either dependent on or independent of the delay size, since they are based on the existence of a common Krasovsky-Lyapunov functional for all the above-mentioned configurations. Extensions to a class of polytopic systems and to a class of regular time-varying systems are also discussed.Ministerio de Educación DPI2006-00714 y GIC07143-IT-269-07 ; Gobierno Vasco SAIOTEK SPED06UN10 y SPE07UN0

A Switched Approach to Robust Stabilization of Multiple Coupled Networked Control Systems

This paper proposes a switched approach to robust stabilization of a collection of coupled networked controlled systems (NCSs) with node devices acting over a limited communication channel. We suppose that the state information of every subsystem is split into different packets and only one packet of the subsystem can be transmitted at a time. Multiple NCSs with norm-bounded parameter uncertainties and multiple transmissions are modeled as a periodic switched system in this paper. State feedback controllers can be constructed in terms of linear matrix inequalities. A numerical example is given to show that a collection of uncertain NCSs with the problem of limited communication can be effectively stabilized via the designed controller

Robust Stability Analysis for Uncertain Switched Discrete-Time Systems

This paper is concerned with the robust stability for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes

Robust Observer Design for Switched Positive Linear System with Uncertainties

This paper is concerned with the design of a robust observer for the switched positive linear system with uncertainties. Sufficient conditions of building a robust observer are established by using the multiple copositive Lyapunov-krasovskii function and the average dwell time approach. By introducing an auxiliary slack variable, these sufficient conditions are transformed into LMI (linear matrix inequality). A numerical example is given to illustrate the validities of obtained results

FeedNetBack-D04.03 - Design of Robust Variable Rate Controllers

A consequence of the execution of control algorithms on digital distributed platforms is inducing delays, jitter and various limitations in sampling rate from different sources in the control loops. These disturbances should be taken into account in the control algorithms design and tuning. Control systems are often cited as examples of "hard real-time systems" where jitter and deadline violations are strictly forbidden. In fact experiments show that this assumption may be false for closed-loop control. Any practical feedback system is designed to obtain some stability margin and robustness w.r.t. the plant parameters uncertainty. This also provides robustness w.r.t. timing uncertainties: closed-loop systems are able to tolerate some amount of sampling period and computing delays deviations, jitter and occasional data loss without loss of stability or integrity. Hence the design of dependable distributed control systems may rely on robust controllers, i.e. controllers which are slightly sensitive to both process model and execution resource uncertainties, or on controllers which are made adaptive w.r.t. the variations of the control intervals and other implementation induced disturbances. Section 2 provides new results concerning the control of systems with delays. A novel analysis of linear systems under asynchronous sampling is provided. This approach is based on the discrete-time Lyapunov Theorem applied to the continuous-time model of the sampled-data systems. Tractable conditions are derived to ensure asymptotic stability and also to obtain an estimate of the exponential rate of the solutions. Examples show the efficiency of the method and the reduction of the conservatism compared to other results from the literature. Moreover the methodology addresses the stability analysis of systems under several sampling periods. We show that a sampled-data system can be stable even if one of the sampling period leads to instability. This has been treated by a continuous-time approach and allows considering uncertain or time-varying systems. An extension of the method includes transmission delays in the control loop. As the variations of the control intervals can be both a consequence of network induced delays and a control variable to manage the CPU and/or network load, robust variable sampling control design is investigated in section 3. Here it is assumed that the control interval is itself a control parameter, e.g. which can be adapted at run-time by a feedback scheduler to cope with operating conditions in a varying environment. The control design is stated using the formulation of Linear Parameters Varying (LPV) systems, where the sampling interval is considered as a varying and measurable parameters of the system. Previous results using a polytopic model of a discretized plant are recalled. A new design using a Linear Fractional Transform (LFT) is developed, where the control interval is considered as a system's uncertainty. This new approach is expected to be more tractable that the polytopic one when the system has several varying parameters. Both designs are assessed and compared using as testbed the control of Autonomous Underwater Vehicles using scheduled ultrasonic sensors for control and navigation.

Robust Hinf tracking control design for a class of switched linear systems using descriptor redundancy approach

International audienceThe work presented in this paper concerns the output feedback tracking control for a class of Switched Linear Systems (SLS) with external disturbances. The main result is based on a descriptor redundancy formulation of the closedloop dynamics. The proposed approach allows the avoiding of the crossing terms appearance between the controller's and the switched system's matrices leading to easier Linear Matrix Inequality (LMI) formulation. Multiple Lyapunov functional methods are utilized to the stability analysis and controller design. By introducing the Proportional-Derivative (PD) controller, a robust Hinf output feedback tracking performance has been satisfied. The efficiency of the proposed synthesis procedure has been illustrated by a numerical example

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