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

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

ISBN-10: 3319288466

ISBN-13: 9783319288468

ISBN-10: 3319288474

ISBN-13: 9783319288475

The booklet addresses the keep an eye on matters reminiscent of balance research, keep watch over synthesis and clear out layout of Markov leap platforms with the above 3 kinds of TPs, and therefore is especially divided into 3 elements. half I reviews the Markov leap structures with partly unknown TPs. various methodologies with diverse conservatism for the fundamental balance and stabilization difficulties are constructed and in comparison. Then the issues of kingdom estimation, the keep watch over of platforms with time-varying delays, the case concerned with either partly unknown TPs and unsure TPs in a composite method also are tackled. half II bargains with the Markov leap platforms with piecewise homogeneous TPs. Methodologies that could successfully deal with keep watch over difficulties within the situation are constructed, together with the only dealing with the asynchronous switching phenomenon among the at present activated method mode and the controller/filter to be designed. half III specializes in the Markov leap platforms with reminiscence TPs. the concept that of σ-mean sq. balance is proposed such that the steadiness 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 sensible examples are given to ensure the effectiveness of the got theoretical effects. ultimately, a few views and destiny works are offered to finish the book.

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**Extra info for Analysis and Design of Markov Jump Systems with Complex Transition Probabilities**

**Sample text**

The corresponding system is stochastically stable if and only if there exists a set of matrices Pi > 0, i ∈ I, such that, ∀i ∈ I, (i) (i) (i) − λ(i) Ai Pi + Pi Ai + PK K Pj < 0, ∀j ∈ IU K , if i ∈ IK Ai Pi + Pi Ai + (i) where PK element. 6) holds. (i) 1. Case 1: i ∈ IK . It should be first noted that in this case one has λ(i) K ≤ 0. We only need to consider (i) λ(i) < 0 here since λ = 0 means the elements in the ith row of the TRM are K K known. 6) as (i) Ai Pi + Pi Ai + PK + Θi (i) = Ai Pi + Pi Ai + PK − λ(i) K (i) j∈IU K λˆ ij Pj λˆ ij (i) j∈IU K −λ(i) K Pj where the elements λˆ ij , ∀j ∈ IU(i)K , are unknown.

The H∞ state-feedback and H∞ dynamic output feedback control problems are treated and LMI conditions are developed to synthesize the H∞ noise attenuation level. Further, the idea of partially unknown TRs are used to improve the modeling for the variations of TRs. In Chap. 7, the estimation problem of the piecewise homogeneous MJSs will be investigated. First, a generalized framework of the H∞ estimation problem is proposed, which can cover both cases of arbitrary and stochastic variation among finite piecewise homogeneous TPs.

Applications of the underlying system with partially unknown TPs in neural networks are presented in [154–156], etc. In addition, the results proposed in [142] are extended to the filter design, fault detection and model reduction of the underlying systems in [157–159], respectively. In terms of finite-time stability, the finite-time H∞ filtering problem is treated in [160]. Many delay-dependent and delay-independent filtering strategies have been 18 1 Introduction developed, such as [161–164] for time-delay neural networks, [165] for singular systems, [166] for systems with nonlinear terms.

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

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