Download Analysis and Design of Singular Markovian Jump Systems by Guoliang Wang, Qingling Zhang, Xinggang Yan PDF

By Guoliang Wang, Qingling Zhang, Xinggang Yan

This monograph is an updated presentation of the research and layout of singular Markovian bounce structures (SMJSs) within which the transition cost matrix of the underlying platforms is usually doubtful, partly unknown and designed. the issues addressed contain balance, stabilization, H∞ keep watch over and filtering, observer layout, and adaptive regulate. purposes of Markov strategy are investigated through the use of Lyapunov concept, 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 common transition price matrices (TRMs);

· stabilization for SMJSs by means of TRM layout, noise keep an eye on, proportional-derivative and in part mode-dependent keep watch over, by way of LMIs with and with out equation constraints;

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

· observer-based controllers of SMJSs within 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 filter out parameters resulting in a mode for completely mode-independent filtering

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

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

Analysis and layout of Singular Markovian bounce Systems comprises worthwhile reference fabric for tutorial researchers wishing to discover the realm. The contents also are compatible for a one-semester graduate course.

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Additional resources for Analysis and Design of Singular Markovian Jump Systems

Sample text

Then, E T Pi = PiT E = E T P¯i E ∈ 0. 17) Since P¯i > 0 and Q¯ i are non-singular, E LT P¯i E L > 0. 1. 9) can be obtained. 25δii2 T¯i − δii W¯ i + ρi j X iT E T (P j − Pi )X i . 19). This completes the proof. 1). 22) where ⎢ ⎣ ≤ ≤ ≤ ≤ Δˆ i2 = πi1 PiT , . . , πi(i−1) PiT πi(i+1) PiT , . . , πi N PiT , Δˆ i3 = −diag{(P1 )Π − ε1 I, . . , (Pi−1 )Π − εi−1 I, (Pi+1 )Π − εi+1 I, . . , (PN )Π − ε N I }. 2 Robust Stabilization 57 Then, the corresponding gain is given as K i = Yi Pi−1 . 1). 25)  where ⎢ ⎣ ≤ ≤ ≤ ≤ Δˇ i2 = πi1 X iT , .

IEEE Trans Autom Control 55:1695–1701 15. Feng JE, Lam J, Shu Z (2010) Stabilization of Markovian systems via probability rate synthesis and output feedback. IEEE Trans Autom Control 55:773–777 16. Boukas EK (2008) Control of Singular Systems with Random Abrupt Changes. Springer, Berlin 17. Xu SY, Lam J (2006) Control and filtering of singular systems. Springer, Berlin 18. Xia YQ, Boukas EK, Shi P, Zhang JH (2009) Stability and stabilization of continuous-time singular hybrid systems. Automatica 45:1504–1509 19.

A(rt ) and B(rt ) are known matrices with compatible dimensions. 3). In this section, the TRM ω is assumed exact known obtained and described by Case 2. © Springer International Publishing Switzerland 2015 G. 11). 1 [1] Let P¯i ∞ Rn×n be symmetric satisfying E LT P¯i E L > 0 and Q¯ i ∞ R(n−r )×(n−r ) be non-singular for each i ∞ S. 5) where U ∞ R(n−r )×n is any matrix with full row rank and satisfies U E = 0; V ∞ Rn×(n−r ) is any matrix with full column rank and satisfies E V = 0. Matrix E is decomposed as E = E L E RT with E L ∞ Rn×r where E R ∞ Rn×r are of full column rank.

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