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Discrete control systems

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New results on robust energy-to-peak filtering for discrete-time switched polytopic linear systems with time-varying delay
Author(s): J. Qiu, G. Feng, J. Yang
Source: IET Control Theory & Applications, Volume 2, Issue 9, 2008 , p. 795 - 806
Type: Article
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The problem of delay-dependent robust energy-to-peak filtering design for a class of discrete-time switched linear systems with a time-varying state delay and polytopic uncertainties is revisited. The objective is to design a homogeneous switched linear filter guaranteeing the exponential stability of the resulting filtering error system with a minimised robust energy-to-peak disturbance attenuation level under average dwell-time switching scheme. Based on a novel delay and parameter-dependent discontinuous switched Lyapunov–Krasovskii functional combined with Finsler's lemma, a new sufficient condition for robust exponential stability and energy-to-peak performance analysis is first derived and then the corresponding filter synthesis is developed. It is shown that the filter parameters can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the advantages and less conservatism of the proposed approach in comparison with the existing approaches.

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Robust mixed ℋ2/ℋ∞ filtering design for discrete-time switched polytopic linear systems
Author(s): J. Qiu, G. Feng, J. Yang
Source: IET Control Theory & Applications, Volume 2, Issue 5, 2008 , p. 420 - 430
Type: Article
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The authors deal with mode and parameter-dependent robust mixed ℋ2/ℋ∞ filtering design for a class of discrete-time switched polytopic linear systems. The objective is to design a homogeneous switched mixed ℋ2/ℋ∞ filter guaranteeing the asymptotic stability of the resulting filtering error systems with given performance measures. Based on a switched parameter-dependent Lyapunov function combined with Finsler's lemma, some novel conditions for robust ℋ2 and ℋ∞ performance analysis are proposed and in turn the filter synthesis is developed. It is shown that by using a new linearisation technique combined with a bounding approach, the filter gains can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.

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