By Zheng-Guang Wu
Singular time-delay structures are very appropriate to explain loads of sensible structures resembling production platforms, networked keep watch over structures, strength platforms and electric circuits. therefore, the previous twenty years have witnessed an important development at the thought of singular time-delay platforms, and lots of primary and critical issues were effectively investigated together with balance research, stabilization, assured fee regulate, filtering, observer layout, sliding mode keep an eye on and so forth. the most goal of this e-book 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 e-book are in most cases in line with examine result of the authors. This ebook should be of curiosity to educational researchers operating in singular platforms, time-delay platforms and Markov leap structures and to graduate scholars attracted to platforms and keep watch over theory.
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Additional info for Analysis and Synthesis of Singular Systems with Time-Delays
1. 2. 20. 5 . 051 In this example, we assume that the time delay d = 5. The purpose is the design of a state feedback controller such that, for all uncertainties, the resultant closed-loop system is regular, impulse free and stable. 05. 3725 . 5579 While the result of  fails to give the desired state feedback controller. Therefore, the result in this chapter improves the existing one. 5 Conclusion The delay-dependent and delay-independent robust control problems for discrete-time SSs with time delay and norm bounded parametric uncertainties have been studied by introducing a ﬁnite sum inequality.
1) with u(t) ≡ 0 to be regular, impulse free, and stable while satisfying a prescribed H∞ performance γ. 2. 4) where R ∈ Rn×(n−r) is any matrix with full column and satisﬁes E T R = 0, and Ξ11 = T1T A + AT T1 + E T P2 + P2T E + Q − E T Z3 E + d2 Z1 , Ξ12 = E T P1 + SRT − T1T + AT T2 + d2 Z2 , Ξ13 = T1T Ad + E T Z3 E − E T P2 , Ξ14 = P3 − E T Z2T , Ξ22 = − T2 − T2T + d2 Z3 , Ξ33 = − Q − E T Z3 E, Ξ34 = − P3 + E T Z2T . Proof. 1) with u(t) ≡ 0 is regular, impulse free and stable. 1). 4) that ⎤ ⎡ ⎤ ⎡ Ξ11 Ξ12 Ξ13 Z1 Z2 0 ⎣ ∗ Ξ22 T2T Ad ⎦ − d2 ⎣ ∗ Z3 0⎦ < 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. 10. 7 . 5. 1 lists the allowable upper bound d2 for various d1 by diﬀerent methods.