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 booklet addresses the keep an eye on concerns comparable to balance research, keep watch over synthesis and filter out layout of Markov leap platforms with the above 3 sorts of TPs, and therefore is principally divided into 3 components. half I reports the Markov bounce structures with partly unknown TPs. various methodologies with assorted conservatism for the fundamental balance and stabilization difficulties are built and in comparison. Then the issues of nation estimation, the keep watch over of structures with time-varying delays, the case concerned with either partly unknown TPs and unsure TPs in a composite approach also are tackled. half II bargains with the Markov leap platforms with piecewise homogeneous TPs. Methodologies which may successfully deal with regulate difficulties within the situation are built, together with the single dealing with the asynchronous switching phenomenon among the at the moment activated procedure mode and the controller/filter to be designed. half III makes a speciality of the Markov leap platforms with reminiscence TPs. the idea that of σ-mean sq. balance is proposed such that the steadiness challenge should 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 got theoretical effects. eventually, a few views and destiny works are offered to finish the book.

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Analysis and Design of Markov Jump Systems with Complex Transition Probabilities

The publication addresses the regulate matters equivalent to balance research, keep watch over synthesis and filter out layout of Markov bounce platforms with the above 3 kinds of TPs, and therefore is principally divided into 3 elements. half I experiences the Markov bounce platforms with in part unknown TPs. diverse methodologies with assorted conservatism for the fundamental balance and stabilization difficulties are built and in comparison.

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15) simultaneously hold. 15) when j = i, ∀j ∈ IU(i)K . 12). 12) hold for i ∈ IK (i) and i ∈ IU K , respectively. 7. 11). 16). Note that the obtained conditions are without loss of generality since the lower bound, λ(i) d , of λˆ ii is allowed to be arbitrarily negative. 3). 3). 18) πij Pj . 7) holds. 18) hold. 3), which completes the proof. 7), the classical criterion to check the stochastic (i) = ∅, ∀i ∈ I, the system stability for the usual discrete-time MJLS. Also, if IK becomes a discrete-time switching linear system under arbitrary switching.

17)), together with some requirements on the latent quadratic Lyapunov function Vi (xt , t) = xt Pi xt , ∀i ∈ I (respectively, Vi (xk , k) = xk Pi xk , ∀i ∈ I). 9), respectively), which implies V˙i (xt , t) < 0 and Vj (xt , t) ≤ Vi (xt , t). 18). 2) with partially unknown TPs. 3). 19) πij Pj . (i) ≤ 1 in the discrete-time case, and we exclude Proof It should be first noted that πK (i) = 1 here since it means that all the elements in the ith row are known. 6 can be rewritten as (i) Ai PK + i (i) j∈IU K (i) (i) = Ai PK + 1 − πK πˆ ij Pj Ai − Pi πˆ ij (i) j∈IU K (i) 1 − πK where the elements πˆ ij , j ∈ IU(i)K , are unknown.

7) holds. 18) hold. 3), which completes the proof. 7), the classical criterion to check the stochastic (i) = ∅, ∀i ∈ I, the system stability for the usual discrete-time MJLS. Also, if IK becomes a discrete-time switching linear system under arbitrary switching. 18) are reduced to Ai Pj Ai − Pi < 0, which is the criterion obtained in [188] by a switched Lyapunov function approach to guarantee the system is globally uniformly asymptotically stable in discrete-time context. 17)), together with some requirements on the latent quadratic Lyapunov function Vi (xt , t) = xt Pi xt , ∀i ∈ I (respectively, Vi (xk , k) = xk Pi xk , ∀i ∈ I).

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