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By Zheng-Guang Wu

Singular time-delay structures are very appropriate to explain loads of useful platforms akin to production structures, networked keep an eye on structures, energy platforms and electric circuits. hence, the earlier twenty years have witnessed an important growth at the idea of singular time-delay structures, and lots of primary and critical subject matters were effectively investigated together with balance research, stabilization, assured expense regulate, filtering, observer layout, sliding mode keep watch over and so forth. the most target of this ebook is to give the most recent advancements and references within the research and synthesis of singular time-delay platforms without or with Markov leaping parameters in a unified framework. The fabrics followed during this publication are ordinarily in accordance with learn result of the authors. This ebook might be of curiosity to educational researchers operating in singular structures, time-delay platforms and Markov leap structures and to graduate scholars attracted to platforms and regulate theory.

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11) which implies A22 is nonsingular. Therefore, the pair (E, A) is regular and impulse free. 1) is regular and impulse free. 1). 12) where V1 (xt ) = Ex(t) t x(α)dα t−d T P1 P2 P2T P3 Ex(t) , x(α)dα t t−d t x(α)T Qx(α)dα, V2 (xt ) = t−d 0 V3 (xt ) = d −d t t+β x(α) E x(α) ˙ T Z1 Z2 ∗ Z3 x(α) dαdβ, E x(α) ˙ where xt = x(t + θ), −2d θ 0. 14) x(t) E x(t) ˙ Z1 Z2 ∗ Z3 x(α) dα. 15) On the other hand, for any appropriately dimensional matrices T1 and T2 , the following equation is true: T T ˙ T2 [E x(t) ˙ + Ax(t) + Ad x(t − d)] α(t) = 2 x(t)T T1T + (E x(t)) = 0.

Synth. of Singular Syst. with Time-Delays, LNCIS 443, pp. 53–69. 1007/978-3-642-37497-5_5 54 5 Dissipativity Analysis for SSs with Time-Varying Delays the delay partitioning method. Some delay-dependent conditions have been established to guarantee the dissipativity of SSs. All the results given in this chapter are delay-dependent as well as partition dependent. Some examples are given to show the validness and reduced conservatism of the proposed methods. 1) where x(t) ∈ Rn is the state, u(t) ∈ Rm is the control input, z(t) ∈ Rs is the controlled output, ω(t) ∈ Rp is the disturbance input that belongs to L2 [0, ∞), and φ(t) ∈ Cn,d2 is a compatible vector valued initial function.

3. 2, which is formulated by strict LMI with the coefficient matrices of the original system. Thus, the BRL is contrast to those of [3, 166, 187, 200, 213], where some nonstrict LMI conditions have been reported, and is also different from the conditions of [38, 193], where the decomposition of the given systems has been used. Testing such a strict LMIbased condition can avoid some numerical problems arising from equality constraints and decomposition of the original system. Thus, the BRL in this chapter is more elegant and has computational advantages from the mathematical point of view.

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