Analysis and Design of Singular Markovian Jump Systems - download pdf or read online

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By Guoliang Wang, Qingling Zhang, Xinggang Yan

ISBN-10: 3319087223

ISBN-13: 9783319087221

ISBN-10: 3319087231

ISBN-13: 9783319087238

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

Features of the publication include:

· learn of the soundness challenge for SMJSs with common transition price matrices (TRMs);

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

· mode-dependent and mode-independent H∞ keep an eye on strategies 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 sturdy H∞ filtering by way of doubtful TRM or clear out parameters resulting in a mode for absolutely 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 approach on singular platforms with norm bounded uncertainties and time-varying delays

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

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Extra resources for Analysis and Design of Singular Markovian Jump Systems

Sample text

3 Robust Stability 49 Fig. 1 DC motor controlling an inverted pendulum where {rt , t ∈ 0} is a Markov process taking values in a finite set S = {1, 2}. 156) becomes a normal SPS with Markovian switching, which is described as  x˙ (t) = x2 (t),   1  g N Km z(t), x˙2 (t) = sin x1 (t) +  l ml 2   ω z˙ (t) = −K b N x2 (t) − R(rt )z(t) + u(t). 1 Vs/rad, Ra = 1Ω and Rb = 2Ω. 5 . 7 For this case, it is also seen that the methods in [21–23, 30] fail in giving an estimation of stability bound ω¯ .

Similarly, the following theorems can be obtained directly. 38) E T P j E − E T Pi E − Wi ≥ 0, i ∞ S, j ∞ S¯ ik , j = i. 42) 26 2 Stability E T P j − E T Pi − Wi ≥ 0, i ∞ S, j ∞ S¯ ik , j = i. 43) πi j Wi , j∞Sik ⎛ ⎝ πi j E T (P j − Pi ) + Wi − τ Wi . 46) AiT G i AiT G i ⎡ρ ⎡ρ + πi j E T (P j − Pi )E + j∞Sik , j =i + πi j Wi , j∞Sik ⎛ ⎝ πi j E T (P j − Pi )E + Wi − τ Wi < 0. 1) under Case 4. From the criteria given above, it is seen that although the TRM may be exact known, uncertain or partially unknown, the proposed methods are all based on a precondition that all or some elements of an TRM are given beforehand.

IEEE Trans Signal Process 54:1421–1430 10. Wang GL, Zhang QL (2013) Robust H⊆ control of Markovian jump systems with uncertain switching probabilities. Asian Journal Control 14:1407–1410 11. Zhang LX, Boukas EK (2009) Mode-dependent H⊆ filtering for discrete-time Markovian jump linear systems with partly unknown transition probability. Automatica 45:1462–1467 52 2 Stability 12. Zhang LX, Boukas EK (2009) Stability and stabilization of Markovian jump linear systems with partly unknown transition probability.

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


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