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

ISBN-10: 3319288466

ISBN-13: 9783319288468

ISBN-10: 3319288474

ISBN-13: 9783319288475

The publication addresses the regulate matters akin to balance research, keep watch over synthesis and filter out layout of Markov bounce structures with the above 3 different types of TPs, and therefore is especially divided into 3 elements. half I stories the Markov bounce structures with partly unknown TPs. diverse methodologies with diversified conservatism for the elemental balance and stabilization difficulties are built and in comparison. Then the issues of country 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 method also are tackled. half II bargains with the Markov leap structures with piecewise homogeneous TPs. Methodologies which could successfully deal with keep watch over difficulties within the state of affairs are constructed, together with the single dealing with the asynchronous switching phenomenon among the presently activated procedure mode and the controller/filter to be designed. half III specializes in the Markov bounce structures 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 platforms concerned with nonlinear dynamics (described through the Takagi-Sugeno fuzzy version) also are investigated. Numerical and functional examples are given to ensure the effectiveness of the received theoretical effects. eventually, a few views and destiny works are provided to finish the book.

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19) holds. 19). 11. 1) with control input u(t). 5). 3). 23) where (i) SK XK(i) λiK(i) Xi , . . , λiKm(i) Xi 1 diag{XK(i) , . . 25) with K1(i) , . . 5) such that the resulting system is stochastically stable. 10), respectively. 21) for i ∈ / IK , respectively. 22). 23). 7 such that the underlying system is stochastically stable. 26). This completes the proof. 16 will not be i checked simultaneously due to the fact IK ∩ IUi K = ∅. 5). 3). 28) Ai Xi + Xi Ai + Bi Yi + Yi Bi and XK(i) TK(i) diag XK1 , .

Now, to establish the H∞ performance for the system, consider the following performance index: J ∞ E e (k)e(k) − γ 2 w (k)w(k) k=0 under zero initial condition, V (x(k), ˜ rk ) |k=0 = 0, and we have ∞ J≤E ∞ = where ζ(k) k=0 k=0 x˜ (k) w (k) i e (k)e(k) − γ 2 w (k)w(k) + ζ (k) V i ζ(k) and A˜ i P¯ i B˜ i + C˜ i D˜ i A˜ i P¯ i A˜ i − Pi + C˜ i C˜ i 2 ∗ −γ I + B˜ i P¯ i B˜ i + D˜ i D˜ i P¯ i πi j P j + i j∈IK By Schur complement, i πi j P j = PK + i j∈IU K i < 0 is equivalent to: ⎡ i πi j P j i j∈IU K −P¯ i ⎢ ∗ ⎢ ⎣ ∗ ∗ ⎤ 0 P¯ i A˜ i P¯ i B˜ i −I C˜ i D˜ i ⎥ ⎥ < 0.

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. 13) As λˆ ii is lower bounded by λ(i) d , we have (i) ˆ λ(i) d ≤ λii < −λK (i) which implies that λˆ ii may take any value between [λ(i) d , −λK + ] for some < 0 arbitrarily small. Then λˆ ii can be further written as a convex combination (i) λˆ ii = −αλ(i) K + α + (1 − α)λd where α takes value arbitrarily in [0, 1] .

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

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