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Delay-range-dependent and delay-distribution-independent stability criteria for discrete-time singular Markovian jump systems

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  • Control Theory
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Abstract

The problem of delay-range-dependent stability for discrete-time singular Markovian jump systems with time-varying delay is discussed in this paper. Based on time-delay partitioning technique, a new delay-range-dependent Lyapunov functional is established firstly. Then, based on the probability idea, LMIs-based delay-range-dependent and delay-distribution-independent conditions are proposed for the system to be regular, causal, and stochastically stable. Furthermore, in terms of solving a set of coupled LMIs, the stabilizing controller is obtained such that the closed-loop system is regular, causal, and stochastically stable. Finally, numerical examples are given to show the results derived from the proposed methods are less conservative than the existing ones.

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Authors and Affiliations

  1. State Key Lab of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, 310027, China

    Falu Weng & Weijie Mao

  2. Jiangxi University of Science and Technology, Jiangxi, 341000, China

    Falu Weng

Authors
  1. Falu Weng
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  2. Weijie Mao
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Correspondence to Weijie Mao.

Additional information

Recommended by Editorial Board member Young Ik Son under the direction of Editor Poogyeon Park.

This work was supported by the National Natural Science Foundation of China (No. 61074045) and the Zhejiang Provincial Natural Science Foundation of China (No. LR12F03002).

Falu Weng received his Master degree in Mechanical Engineering and Automation from Jiangxi University of Science and Technology, China, in 2005. Now, he is a Ph.D. candidate at the Department of Control Science and Engineering, Zhejiang University, China. His research interests include robust control, singular systems, time-delay systems and applications.

Weijie Mao received his Ph.D. degree in Control Science and Engineering from Zhejiang University, China, in 1996. Currently, he is a professor at the Department of Control Science and Engineering, Zhejiang University. His research interests include robust control, singular systems, time-delay systems, decoupling control theory and applications.

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Weng, F., Mao, W. Delay-range-dependent and delay-distribution-independent stability criteria for discrete-time singular Markovian jump systems. Int. J. Control Autom. Syst. 11, 233–242 (2013). https://doi.org/10.1007/s12555-012-0200-4

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  • DOI: https://doi.org/10.1007/s12555-012-0200-4

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