Download PDF by Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu: Analysis and Design of Markov Jump Systems with Complex

By Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu

ISBN-10: 3319288466

ISBN-13: 9783319288468

ISBN-10: 3319288474

ISBN-13: 9783319288475

The ebook addresses the keep watch over matters akin to balance research, keep an eye on synthesis and filter out layout of Markov leap structures with the above 3 forms of TPs, and hence is especially divided into 3 elements. half I reviews the Markov leap structures with in part unknown TPs. various methodologies with assorted conservatism for the fundamental balance and stabilization difficulties are built and in comparison. Then the issues of kingdom estimation, the keep an eye on of platforms with time-varying delays, the case concerned with either in part unknown TPs and unsure TPs in a composite approach also are tackled. half II offers with the Markov leap structures with piecewise homogeneous TPs. Methodologies that could successfully deal with keep watch over difficulties within the situation are constructed, together with the single dealing with the asynchronous switching phenomenon among the at present activated procedure mode and the controller/filter to be designed. half III makes a speciality of the Markov leap structures with reminiscence TPs. the idea that of σ-mean sq. balance is proposed such that the soundness challenge could be solved through a finite variety of stipulations. The platforms concerned with nonlinear dynamics (described through the Takagi-Sugeno fuzzy version) also are investigated. Numerical and functional examples are given to make sure the effectiveness of the bought theoretical effects. ultimately, a few views and destiny works are offered to finish the book.

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3 ? 5 ? 4 ? 3 ? 1 2 3 4 1 ? 3 ? 2 ? 5 ? 3 ? ? 4 x1 Fig. 2 0 x 1 Fig. 3 ? 2 2 ? 1 ? 3 ? 4 ? 3 ? 3 ? ? 2 ? 2 ? 3 ? 4 ? 3 ? 8 , B2 = , B3 = , B4 = . 2. 4] under two different modes evolution. It is seen from the curves in Figs. 4 that, despite the partially unknown TPs, the designed controllers are feasible and effective ensuring the resulting closed-loop systems are stable, in the continuous-time or in discrete-time cases, respectively. The validity and the reduction of conservatism of the results obtained above are verified by the following numerical examples.

4) where Km(i) ∈ N+ represents the mth known element with the index Km(i) in the ith row of matrix or . Also, throughout the chapter, we denote λ(i) K (i) j∈IK (i) πK λij , (i) j∈IK πij In the continuous-time case, when λˆ ii is unknown, it is necessary to provide a lower (i) (i) bound λ(i) d for it and we have λd ≤ −λK . 1 The accessibility of the jumping process {rt , t ≥ 0} (or {rk , k ≥ 0}) in the existing literature is commonly assumed to be completely accessible (IU(i)K = ∅, (i) (i) IK = I) or completely inaccessible (IK = ∅, IU(i)K = I).

5) such that the closed-loop system is stochastically stable. 26). 19) holds. 19) is equivalent to ⎡ −Pi ∗ ∗ ⎢ √πiK1 PK1 Ai −PK1 ∗ ⎢ √ ⎢ πiK2 PK2 Ai 0 −PK2 ⎢ ⎢ .. .. ⎢ . . ⎢√ ⎢ πiKm PKm Ai 0 0 i i ⎣ (i) 1 − πK Pj Ai 0 0 ∗ ∗ ∗ .. 40). 37). 14, that is, the underlying system is stochastically stable. 26). 22 In contrast with the continuous-time case, the discrete-time case is relatively simpler since all the elements in the TPM are nonnegative and we need not distinguish the cases of diagonal elements known or unknown.

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Analysis and Design of Markov Jump Systems with Complex Transition Probabilities by Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu

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