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By Guoliang Wang, Qingling Zhang, Xinggang Yan

This monograph is an up to date presentation of the research and layout of singular Markovian bounce platforms (SMJSs) within which the transition price matrix of the underlying structures is usually doubtful, partly unknown and designed. the issues addressed contain balance, stabilization, H∞ regulate and filtering, observer layout, and adaptive keep an eye on. purposes of Markov procedure are investigated by utilizing Lyapunov idea, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, between different techniques.

Features of the booklet include:

· examine of the soundness challenge for SMJSs with normal transition expense matrices (TRMs);

· stabilization for SMJSs by means of TRM layout, noise keep an eye on, proportional-derivative and in part mode-dependent regulate, when it comes to LMIs with and with out equation constraints;

· mode-dependent and mode-independent H∞ regulate recommendations with improvement of one of those disordered controller;

· observer-based controllers of SMJSs during which either the designed observer and controller are both mode-dependent or mode-independent;

· attention of strong H∞ filtering by way of doubtful TRM or clear out parameters resulting in a style for absolutely mode-independent filtering

· improvement of LMI-based stipulations for a category of adaptive country suggestions controllers with almost-certainly-bounded envisioned blunders and almost-certainly-asymptotically-stable corresponding closed-loop method states

· purposes of Markov method on singular platforms with norm bounded uncertainties and time-varying delays

Analysis and layout of Singular Markovian bounce Systems includes beneficial reference fabric for educational researchers wishing to discover the world. The contents also are compatible for a one-semester graduate course.

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Extra info for Analysis and Design of Singular Markovian Jump Systems

Sample text

Stochast Anal Appl 20:33–92 2. Feng X, Loparo KA, Ji Y, Chizeck HJ (1992) Stochastic stability properties of jump linear systems. IEEE Trans Autom Control 37:38–53 3. Huang LR, Mao XR (2010) On almost srue stability of hybrid stochastic systems with modedependent interval delays. IEEE Trans Autom Control 55:1946–1952 4. Mao XR (1999) Stability of stochastic differential equations with Markovian switching. Stochastic Processes their Appl 79:45–67 5. Mao XR (2002) Exponential stability of stochastic delay interval systems with Markovian switching.

The main objective of stabilization problem is to synthesise a controller such that the resultant closed-loop system is stable with desired performances. In this chapter, the stabilization problem for SMJSs is concerned. Because singular derivative matrix and Markov property are included in SMJSs simultaneously, they usually make the synthesis for SMJSs with general conditions much complicated. The purpose of this chapter is to design some kinds of controllers such that the closed-loop system is regular, impulse-free and stable.

IEEE Trans Autom Control 47:1604–1612 6. Boukas EK, Shi P, Benjelloun K (1999) On robust stabilization of uncertain linear systems with jump parameters. Int J Control 72:842–850 7. Mahmound MS, Shi P (2003) Robust stability, stabilization and H⊆ control of time-delay systems with Markovian jump parameters. Int J Robust Nonlinear Control 13:755–784 8. Xiong JL, Lam J (2006) On robust stabilization of Markovian jump systems with uncertain switching probabilities. Automatica 41:897–903 9. Xiong JL, Lam J (2006) Fixed-order robust H⊆ filter design for Markovian jump systems with uncertain switching probabilities.

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