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Analysis and Design of Singular Markovian Jump Systems by Guoliang Wang, Qingling Zhang, Xinggang Yan

By Guoliang Wang, Qingling Zhang, Xinggang Yan

This monograph is an up to date presentation of the research and layout of singular Markovian leap structures (SMJSs) during which the transition expense matrix of the underlying platforms is usually doubtful, partly unknown and designed. the issues addressed comprise balance, stabilization, H∞ keep an eye on and filtering, observer layout, and adaptive regulate. purposes of Markov procedure are investigated through the use of Lyapunov concept, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, between different techniques.

Features of the e-book include:

· research of the soundness challenge for SMJSs with basic transition cost matrices (TRMs);

· stabilization for SMJSs by means of TRM layout, noise keep an eye on, proportional-derivative and partly mode-dependent keep an eye on, when it comes to LMIs with and with no equation constraints;

· mode-dependent and mode-independent H∞ regulate recommendations with improvement of a kind of disordered controller;

· observer-based controllers of SMJSs within which either the designed observer and controller are both mode-dependent or mode-independent;

· attention of strong H∞ filtering when it comes to doubtful TRM or filter out parameters resulting in a style for completely mode-independent filtering

· improvement of LMI-based stipulations for a category of adaptive nation suggestions controllers with almost-certainly-bounded predicted blunders and almost-certainly-asymptotically-stable corresponding closed-loop process states

· purposes of Markov strategy on singular structures with norm bounded uncertainties and time-varying delays

Analysis and layout of Singular Markovian leap Systems includes necessary reference fabric for educational researchers wishing to discover the realm. The contents also are compatible for a one-semester graduate course.

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Extra resources for Analysis and Design of Singular Markovian Jump Systems

Sample text

Part of the results presented in this chapter are available in [31, 32]. References 1. Drˇagan V, Morozan T (2000) Stability and robust stabilization to linear stochastic systems described by differential equations with Markovian jumping and multiplicative white noise. Stochast Anal Appl 20:33–92 2. Feng X, Loparo KA, Ji Y, Chizeck HJ (1992) Stochastic stability properties of jump linear systems. IEEE Trans Autom Control 37:38–53 3. Huang LR, Mao XR (2010) On almost srue stability of hybrid stochastic systems with modedependent interval delays.

73) with any compatible initial condition on [t0 , t1 ). Similarly, it can be also shown that there is a unique solution on [t1 , t2 ) for any given admissible condition ξ(t1 ), and so on. So it is obtained that Eq. 74) has a unique solution on [0, ⊆). This completes the proof. 25ωii2 Si3 − ωii Ui3 + τ γi2 G i1 G i1 + G i2 G i2 , Ωi1 = Pi4 Bi2 , ⎪ ⎡ρ 11 T Ωi2 = Ai1 Pi5 E + N εi j E T (P j5 − Pi5 )E, j=1, j =i ⎪ ⎡ T εi j E T P j3 − Pi3T , N 12 T T T Ωi2 =Ai1 Pi3 + Ai3 Pi6 + E T Pi5 Ai2 + j=1, j =i ⎪ 13 22 T Ωi2 =E T Pi5 Bi1 , Ωi2 = Ai4 Pi6 ⎡ρ N + (Pi3 Ai2 )ρ + εi j (P j4 − Pi4 ), j=1, j =i N 23 24 1 =Pi3 Bi1 , Ωi2 = Pi6 Bi2 , Ωi3 = Ωi2 εi j (P j6 − Pi6 ).

73). 2 For any given ω > 0, the pair (E ω , A(rt )) is said to be: (1) regular if det(s E ω − A(rt )) is not identically zero for every rt ∞ S; (2) impulse-free if deg(det(s E ω − A(rt ))) = rank(E ω ) for every rt ∞ S. 74) is said to be exponentially meansquare stable, if there exist scalars a > 0 and b > 0 such that 32 2 Stability E { ξ(t) 2 |ξ0 , r0 } ≥ ae−bt ξ0 2 , for any initial conditions ξ0 ∞ Rn+m and r0 ∞ S. From [17], it is seen that for any given ω > 0, there always exist two non-singular matrices M(ω) and N (ω) such that ⎢ ⎢ 1 ⎦ ⎦ I 0 Aω (rt ) A2ω (rt ) Mω E ω N ω = , Mω Aω (rt )Nω = .

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