Research on Feedback Robust Stabilization Control of Periodic Time-Varying Singular Systems

This work discuss the robust stabilization problem for discrete-time switched singular systems with simultaneous presence of time-varying delay and sensor nonlinearity. To this end, an observer-based controller was synthesized that works under asynchronous switching signals. Investigating the average dwell time approach and using a Lyapunov–Krasovskii functional with triple sum terms, sufficient conditions were derived for achieving the existence of such asynchronous controller and guaranteeing the resulting closed-loop system to be exponentially admissible with H∞ performance level. Subsequently, the effectiveness of the proposed control scheme was verified through two numerical examples.

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Robust Admissibilization for Discrete-Time Singular Systems with Time-Varying Delay

Mathematical Problems in Engineering ◽

10.1155/2019/5368013 ◽

2019 ◽

Vol 2019 ◽

pp. 1-14

Author(s):

Dongdong Wang ◽

Shengzhi Han ◽

Jian Chen

Keyword(s):

Discrete Time ◽

Singular Systems ◽

Robust Stabilization ◽

Feedback Stabilization ◽

Relaxation Techniques ◽

Time Varying ◽

Time Varying Delay ◽

Convex Inequality ◽

Summation Inequality ◽

Varying Delay

The problems of the admissibility and state feedback stabilization for discrete-time singular systems with interval time-varying delay and norm-bounded uncertainty are studied. The system is equivalently transformed into a new comparison form by decomposition. By taking advantage of the Seuret summation inequality, the reciprocally convex inequality, and some relaxation techniques, a delay-dependent criterion that ensures the admissibility of the concerned systems is established. The result on robust stabilization is also obtained by fixing some parameters. It should be pointed out that the results are less dependent on the parameters so that some conservatism is reduced. A numerical example is included to illustrate the effectiveness and improvement of the proposed methods.

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Novel Stabilization Conditions for Uncertain Singular Systems with Time-Varying Delay

Mathematical Problems in Engineering ◽

10.1155/2014/796596 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8

Author(s):

Yuanchun Ding ◽

Falu Weng ◽

Ji Ge ◽

Qi Liang ◽

Xueyi Zhi

Keyword(s):

Singular Systems ◽

Singular System ◽

Robust Stabilization ◽

State Feedback Control ◽

Delay Systems ◽

Time Varying ◽

Time Varying Delay ◽

Uncertain Singular Systems ◽

Delay Dependent ◽

Varying Delay

The problem of delay-dependent robust stabilization for continuously singular time-varying delay systems with norm-bounded uncertainties is investigated in this paper. First, based on some mathematical transform, the uncertain singular system is described in a form which involves the time-delay integral items. Then, in terms of the delay-range-dependent Lyapunov functional and the LMI technique, the improved delay-dependent LMIs-based conditions are established for the uncertain singular systems with time-varying delay to be regular, causal, and stable. Furthermore, by solving these LMIs, an explicit expression for the desired state feedback control law can be obtained; thus, the regularity, causality, and stability of the closed-loop system are guaranteed. In the end, numerical examples are given to illustrate the effectiveness of the proposed methods.

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