Stabilization of discrete-time systems with time-varying delay using simple lyapunov-krasovskii functional

This thesis studies stabilization of discrete time-delay systems based on Lyapunov-Krasovskii functional. Time-delays frequently occur in various practical systems, such as networked control systems, chemical processes, neural networks, and long transmission lines in pneumatic systems. The different phenomena that cause time-delay are: (a) Time needed to transport mass, energy or information; (b) Time lags get accumulated in great number of low-order systems connected in series; and (c) Sensors, such as analyzers; controllers need some time to implement a complicated control algorithm or process. The presence of delay causes in general performance degradation and may lead to instability within the system First, stability of networked control systems has been studied. Two available stability criteria for linear discrete time systems with interval like time varying delay have been considered. Also a numerical example has been solved and the results of both the stability criteria have been compared. Static output-feedback stabilization of discrete-time system with time-varying delay is studied next. Two stabilization approaches based on the above discussed stability criteria are studied. A numerical example has been solved and simulation results have been obtained for both the approaches. Simulation output indicates that the given stabilization approaches effectively stabilize the system and their performance in terms of achievable delay margin is compared

Stochastic H ∞ Finite-Time Control of Discrete-Time Systems with Packet Loss

This paper investigates the stochastic finite-time stabilization and H ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic H ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic H ∞ finitetime stabilization of the class of stochastic systems. The stochastic H ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme

Stochastic ℋ

This paper investigates the stochastic finite-time stabilization and ℋ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic ℋ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic ℋ∞ finite-time stabilization of the class of stochastic systems. The stochastic ℋ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme

Robust stability and stabilization of nonlinear uncertain stochastic switched discrete-time systems with interval time-varying delays,

Abstract: This paper is concerned with robust stability and stabilization of nonlinear uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust stability and stabilization for the nonlinear uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results

Analysis and synthesis of Markov Jump Linear systems with time-varying delays and partially known transition probabilities

In this note, the stability analysis and stabilization problems for a class of discrete-time Markov jump linear systems with partially known transition probabilities and time-varying delays are investigated. The time-delay is considered to be time-varying and has a lower and upper bounds. The transition probabilities of the mode jumps are considered to be partially known, which relax the traditional assumption in Markov jump systems that all of them must be completely known a priori. Following the recent study on the class of systems, a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix. Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory. © 2008 IEEE.published_or_final_versio

Robustness analysis of discrete predictor-based controllers for input-delay systems

In this article, robustness to model uncertainties are analysed in the context of discrete predictor-based state-feedback controllers for discrete-time input-delay systems with time-varying delay, in an LMI framework. The goal is comparing robustness of predictor-based strategies with respect to other (sub)optimal state feedback ones. A numerical example illustrates that improvements in tolerance to modelling errors can be achieved by using the predictor framework.The authors are grateful for grant nos. DPI2008-06737-C02-01, DPI2008-06731-C02-01, DPI2011-27845-C02-01 and PROMETEO/2008/088 from the Spanish and Valencian governments.González Sorribes, A.; Sala, A.; García Gil, PJ.; Albertos Pérez, P. (2013). Robustness analysis of discrete predictor-based controllers for input-delay systems. International Journal of Systems Science. 44(2):232-239. https://doi.org/10.1080/00207721.2011.600469S232239442Boukas, E.-K. (2006). 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International Journal of Systems Science, 39(4), 427-436. doi:10.1080/00207720701832531Yue, D., & Han, Q.-L. (2005). Delayed feedback control of uncertain systems with time-varying input delay. Automatica, 41(2), 233-240. doi:10.1016/j.automatica.2004.09.006Zhang, B., Xu, S., & Zou, Y. (2008). Improved stability criterion and its applications in delayed controller design for discrete-time systems. Automatica, 44(11), 2963-2967. doi:10.1016/j.automatica.2008.04.01

Dynamic Output Feedback Control of Discrete-Time Systems with Actuator Nonlinearities

Abstract This paper considers the problem of stabilization of discrete-time systems with actuator nonlinearities. Specifically, dynamic, output feedback control design for discrete-time systems with time-varying, sectorbounded, input nonlinearities is addressed. The proposed framework is based on a linear matrix inequality approach and directly accounts for robust stability and robust performance over the class of actuator nonlinearities. F'urthermore, it is directly applicable to actuator saturation control and provides dynamic, output feedback controllers with guaranteed domains of attraction. The effectiveness of the approach is illustrated by a numerical example

Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay

This paper is concerned with the problems of stability analysis and stabilization for discrete-time Takagi-Sugeno fuzzy systems with time-varying state delay. By constructing a new fuzzy Lyapunov function and by making use of novel techniques, an improved delay-dependent stability condition is obtained, which is dependent on the lower and upper delay bounds. The merit of the proposed stability condition lies in its reduced conservatism, which is achieved by avoiding the utilization of some bounding inequalities for the cross products between two vectors. Then, delay-dependent stabilization approach based on a parallel distributed compensation scheme is developed for both state feedback and observer-based output feedback cases. The proposed stability and stabilization conditions are formulated in terms of linear matrix inequalities, which can be solved efficiently by using existing optimization techniques. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper. © 2008 IEEE.published_or_final_versio