By Zheng-Guang Wu

ISBN-10: 3642374964

ISBN-13: 9783642374968

ISBN-10: 3642374972

ISBN-13: 9783642374975

Singular time-delay structures are very compatible to explain loads of functional platforms akin to production structures, networked regulate platforms, strength structures and electric circuits. therefore, the earlier twenty years have witnessed an important growth at the conception of singular time-delay structures, and plenty of primary and critical subject matters were effectively investigated together with balance research, stabilization, assured price keep an eye on, filtering, observer layout, sliding mode keep watch over and so forth. the most aim of this publication is to give the most recent advancements and references within the research and synthesis of singular time-delay structures without or with Markov leaping parameters in a unified framework. The fabrics followed during this publication are frequently in line with learn result of the authors. This booklet could be of curiosity to educational researchers operating in singular platforms, time-delay structures and Markov leap structures and to graduate scholars attracted to structures and keep an eye on theory.

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59) over L1 > 0, W , Yˆ , V , Zˆ1 > 0, Zˆ2 > 0, Zˆ3 > 0, Sˆ1 > 0, Sˆ2 > 0 and M = diag{m1 , m2 , · · · , mi } > 0. 9. It is worth pointing out that by applying the similar method, the other conditions of this chapter can also be transformed to strict LMI conditions. Thus, all the developed results in the chapter can be checked easily by using the existing powerful tools like the LMI toolbox of Matlab or any equivalent tool. 4 Numerical Examples In this section, two examples are presented to demonstrate the effectiveness of the results developed in this chapter.

By the free-weighting matrix method, the problems of robust passivity analysis and passivity-based sliding mode control have been addressed for a kind of uncertain singular time-delay systems in [149], where a delay-dependent sufficient condition has been proposed in terms of LMI, which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive, and the passification solvability condition has been also established. It should be mentioned that the involved time delays in [76, 149] are timeinvariant, which limits the scope of applications of the given results.

1). 2 Continuous-Time Systems Υ(t) = x(t)T x(t − η(t) = Υ(t)T x(t 1 T m d1 ) x(t T − d1 )T , − 2 T m d1 ) . . x(t − ζ(t) = η(t)T x(t − d(t))T x(t − d2 )T ω(t)T T m−1 T T m d1 ) 55 , , W1 = Imn 0mn×n , W2 = 0mn×n Imn , gl = 0n×(l−1)n In 0n×(m−l+1)n , l = 1, 2, · · · , m + 1, d12 = d2 − d1 , D= 2 m d1 m Si + d212 Sm+1 . 1) can be rewritten as ⎧ ˙ = Ag1 η(t) + Ad x(t − d(t)) + Bω ω(t), ⎪ ⎨ E x(t) z(t) = Cg1 η(t) + Cd x(t − d(t)) + Dω ω(t), ⎪ ⎩ x(t) = φ(t), t ∈ [−d2 , 0]. 2. 6) 56 5 Dissipativity Analysis for SSs with Time-Varying Delays Ξ33 = − Z1 − E T Sm+1 E, Ξ44 = − R + γI − S T Dω − DωT S.

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Analysis and Synthesis of Singular Systems with Time-Delays by Zheng-Guang Wu


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