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

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

The publication addresses the keep an eye on matters corresponding to balance research, regulate synthesis and filter out layout of Markov bounce platforms with the above 3 different types of TPs, and hence is especially divided into 3 components. half I reviews the Markov leap platforms with partly unknown TPs. varied methodologies with varied conservatism for the fundamental balance and stabilization difficulties are constructed and in comparison. Then the issues of kingdom estimation, the keep watch over of structures with time-varying delays, the case concerned with either in part unknown TPs and unsure TPs in a composite method also are tackled. half II bargains with the Markov leap structures with piecewise homogeneous TPs. Methodologies which could successfully deal with regulate difficulties within the situation are constructed, together with the only dealing with the asynchronous switching phenomenon among the presently 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 will be solved through a finite variety of stipulations. The structures 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 acquired theoretical effects. ultimately, a few views and destiny works are offered to finish the book.

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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. 11) holds. 2. Case 2: i ∈ IU(i)K . (i) ˆ In this case, λˆ ii is unknown, λ(i) K ≥ 0 and λii ≤ −λK . Also, we only consider (i) (i) λˆ ii < −λK here since if λˆ ii = −λK , then the ith row of the TRM is completely known.

Part I: Markov jump systems with partially unknown TPs Chapter 2 discusses the stochastic stability and stabilization problems for continuous-time and discrete-time MJLSs with partially unknown TPs. The relationships among the ideal TPs case, partially unknown TPs case, and the systems under arbitrary switching case are discussed and it has been proved that the results for MJSs with partially unknown TPs can cover the ideal TPs and arbitrary switching cases as special situations. Chapter 3 deals with the H∞ filtering problem for discrete-time MJLS.

N } with a transition probabilities matrix (TPM) = {πi j } namely, for rk = i, rk+1 = j, one has Pr(rk+1 = j|rk = i) = πi j where πi j ≥ 0 ∀ i, j ∈ I, and Nj=1 πi j = 1. 1) and for rk = i ∈ I, the system matrices of the ith mode are denoted by Ai , Bi , Ci , Di , Hi , and L i , which are considered here to be real known with appropriate dimensions. © Springer International Publishing Switzerland 2016 L. , some elements in matrix are unknown. 1) with 4 operation modes, the TPM may be as: ⎡ ⎤ π11 ?

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