Download Filtering and Control of Stochastic Jump Hybrid Systems by Xiuming Yao, Ligang Wu, Wei Xing Zheng PDF

By Xiuming Yao, Ligang Wu, Wei Xing Zheng

This booklet provides fresh study paintings on stochastic leap hybrid platforms. particularly, the thought of stochastic bounce hybrid platforms contain Markovian leap Ito stochastic structures, Markovian leap linear-parameter-varying (LPV) structures, Markovian leap singular structures, Markovian bounce two-dimensional (2-D) structures, and Markovian bounce repeated scalar nonlinear platforms. a few adequate stipulations are first confirmed respectively for the steadiness and performances of these different types of stochastic leap hybrid platforms by way of resolution of linear matrix inequalities (LMIs). in keeping with the derived research stipulations, the filtering and keep watch over difficulties are addressed.

The publication offers updated study advancements and novel methodologies on stochastic leap hybrid platforms. The contents might be divided into components: the 1st half is targeted on strong clear out layout challenge, whereas the second one half is placed the emphasis on strong keep watch over challenge. those methodologies offer a framework for balance and function research, powerful controller layout, and powerful clear out layout for the thought of structures. ideas to the layout difficulties are offered by way of LMIs.

The publication is a well timed mirrored image of the constructing region of filtering and keep watch over theories for Markovian leap hybrid platforms with several types of imperfect info. it's a selection of a chain of contemporary study effects and as a result serves as an invaluable textbook for senior and/or graduate scholars who're attracted to realizing 1) the state of the art of linear filtering and keep an eye on parts, and a pair of) fresh advances in stochastic leap hybrid structures. The readers also will take advantage of a few new ideas, new types and new methodologies with sensible value up to speed engineering and sign processing.

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Extra info for Filtering and Control of Stochastic Jump Hybrid Systems

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6) is robustly stochastically stable with an H∞ performance level γ if there exist matrices Pi > 0, Q > 0, M > 0, U1i , U2i , U3i and scalars ε1i > 0, ε2i > 0, λij > 0 (j = i, j = 1, 2, . . , N ) such that for i = 1, 2, . . 3 Main Results where P¯ i 17 N j=1 π¯ ij Pj and ⎧ Π11i ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ Π12i ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ Π13i Pi A¯ i + A¯ Ti Pi + K T QK + L¯ iT L¯ i + P¯ i + U1i K + (U1i K)T ⎪ Π22i ⎪ ⎪ ⎪ ⎪ ⎪Π ⎪ ⎪ 23i ⎪ ⎪ ⎪ ⎪ ⎪ Π33i ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ Ξi ⎪ ⎪ ⎪ ⎩ Λi N + 1 ¯ T1i G ¯ 1i , λij μ2ij I + (ε1i + ε2i )G 4 j=1,j=i ¯ T1i G2i , Γ12i Γ12i + (ε1i + ε2i )G Pi A¯ di + (U2i K)T − U1i , ¯ T1i G3i , Γ13i Γ13i + (ε1i + ε2i )G Pi B¯ i + (U3i Ki )T , Γ22i + (ε1i + ε2i )GT2i G2i , Γ22i −(1 − h)Q − U2i − U2iT , Γ23i + (ε1i + ε2i )GT2i G3i , Γ23i −U3iT , Γ33i + (ε1i + ε2i )GT3i G3i , Γ33i −γ 2 I, (Pi − P1 ), .

2 Problem Formulation and Preliminaries ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ξk ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ E˜ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ B˜ 1i ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ B˜ 2i ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ˜ ⎪ ⎪ C1i ⎪ ⎪ ⎪ D˜ 1i ⎪ ⎪ ⎪ ⎩ ˜ D2i 49 ⎤ ⎡ ⎤ x¯k uk ⎢ ⎥ ⎢ ⎥ ⎣ xk ⎦ , υk ⎣ ωk ⎦ , ek rk − f¯k , xˆk fk ⎤ ⎤ ⎤ ⎡ ⎡ ⎡ 0 0 AW 0 0 0 I 0 0 ⎥ ⎥ ⎥ ⎢ ⎢ ⎢ Ai 0 ⎦ , A˜ 2i ⎣ 0 0 0 ⎦ , ⎣ 0 E 0 ⎦ , A˜ 1i ⎣ 0 0 0 I 0 αB 0 B f i Ci 0 ¯ f i Ci A f i ⎤ ⎡ 0 0 BW ⎥ ⎢ E 1i E 2i ⎦ , ⎣ Bi αB ¯ f i Di αB ¯ f i F1i αB ¯ f i F2i ⎤ ⎡ 0 0 0 ⎥ ⎢ 0 0 ⎦, ⎣ 0 B f i Di B f i F1i B f i F2i ¯ f i Ci C f i , C˜ 2i −C W αD 0 D f i Ci 0 , ¯ f i F1i αD ¯ f i F2i − DW , αD ¯ f i Di αD D f i Di D f i F1i D f i F2i .

S and θ ∈ , where is the set of allowable parameter trajectories, which is defined s as θ : θj ≤ νj , j = 1, 2, . . , s where νj j=1 are non-negative numbers and ν = ν 1 ν 2 . . νs . The matrices Ai (θ) Ark =i (θ), Bi (θ) Brk =i (θ), Ci (θ) Crk =i (θ), Di (θ) Lrk =i (θ), are known real constant matrices of appropriate Drk =i (θ) and Li (θ) dimensions. Since a communication network links the physical plant and the filter, data packet dropout phenomenon happens unavoidably and the measurements yk drop intermittently, that is, y¯ k = yk , where y¯ k is the measurement received at the mode quantizer q(·).

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