Stability and robust stabilisation for a class of non-linear uncertain discrete-time descriptor Markov jump systems

Author(s): S. Song ; S. Ma ; C. Zhang
DOI: 10.1049/iet-cta.2012.0479

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Author(s): S. Song ¹ ; S. Ma ¹ ; C. Zhang ²
- Affiliations: 1: School of Mathematics, Shandong University, Jinan, People’s Republic of China
  2: School of Control and Engineering, Shandong University, Jinan, People’s Republic of China
Source: Volume 6, Issue 16, 1 November 2012, p. 2518 – 2527
DOI: 10.1049/iet-cta.2012.0479 , Print ISSN 1751-8644, Online ISSN 1751-8652

The stability and robust state feedback stabilisation problems for a class of non-linear discrete-time descriptor Markov jump systems with parameter uncertainties are investigated. The non-linear function satisfies a quadratic constraint. First, based on Lyapunov theory and the implicit function theorem, a linear matrix inequality (LMI) sufficient condition is developed, which guarantees that the non-linear discrete-time descriptor Markov jump systems are regular, causal, and have unique solution in a neighbourhood of the origin, and are stochastically stable. With this condition, another LMI condition is developed based on the singular value decomposition approach, which guarantees that the systems are regular, causal, have unique solution in a neighbourhood of the origin, and are stochastically stable. Then, the design method of robust state feedback controllers is given. Last, numerical examples are provided to illustrate the effectiveness of the proposed methods.

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Stability and robust stabilisation for a class of non-linear uncertain discrete-time descriptor Markov jump systems

Stability and robust stabilisation for a class of non-linear uncertain discrete-time descriptor Markov jump systems

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