Robust H∞ control of discrete switched system with time delay

Department of Engineering and Design, University of Sussex, Brighton BN1 9QT, UK
Applied Mathematics and Computation (Impact Factor: 1.55). 11/2008; 205(1):159-169. DOI: 10.1016/j.amc.2008.05.046
Source: DBLP


This paper deals with the stabilization and robust H-infinity control of discrete switched system with time delay. The switching is time-driven and the design is based on the average dwell time method. The controller parameters and the permissible switching sequence, subject to the given average dwell time, can be obtained by solving a set of linear matrix inequalities (LMIs). Two examples are given to demonstrate the proposed methods.

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    • ", and it has been modified to fit the discrete-time ones in some existing literature (Song et al., 2008). As commonly used in the literature, we choose N 0 = 0 in this paper. "
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    ABSTRACT: This paper is concerned with the exponential stability analysis for a class of discrete-time switched non-linear systems with time-varying delays. By constructing an appropriate Lyapunov–Krasovskii function, a new criterion for checking the exponential stability of the addressed switched systems is established and then formulated in terms of linear matrix inequalities. It is shown that this new criterion can provide less conservative results than some existing ones. Two numerical examples are given to illustrate the effectiveness of the proposed results.
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    ABSTRACT: The switching signal design for H∞ performance of uncertain discrete switched systems with interval delay and linear fractional perturbations is considered in this paper. Some LMI stability criteria are proposed to design the switching signal and guarantee the H∞ performance for discrete switched time-delay system. Some nonnegative inequalities are introduced to improve the conservativeness of the proposed results. A numerical example is illustrated to show the less conservativeness of the main result. Finally, a water quality model is also provided to demonstrate the practical applications of our proposed results.
    Full-text · Article · Feb 2013 · Applied Mathematical Modelling
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    • "The objective of H 1 control is to design controllers such that the closed–loop system is internally stable and its H 1 norm from the external input to the controlled output is less than a prescribed level. Since the theory of H 1 control has proposed by Zames [1], much effort has been made in H 1 controller design in order to guarantee desired stability [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]. However, this control is often based on the assumption that the entire state is available, which may not hold in many systems. "
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    ABSTRACT: This paper investigates the observer-based H∞H∞ control problem for a class of discrete-time mixed delay systems with random communication packet losses and multiplicative noises, where the mixed delays comprise both discrete and distributed time-varying delays, the random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer-based feedback controller are derived, such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H∞H∞ performance. Then a linear matrix inequality (LMI) approach for designing such an observer-based H∞H∞ controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.
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