Delay-dependent robust H∞ control for uncertain systems with a state-delay

Delay-Dependent Robust Stability of Time Delay Systems

“…In all methods h max is obtained by a line search. (Niculescu et al, 1995) 0.99 11 (Moon et al, 2001) 4.3588 16 (Han, 2002) 4.4721 9 or 18 (Fridman, 2002) 4.47 27 (Xu and Lam, 2005) 4.4721 17 (Suplin et al, 2004) 4 Table 1 show that Theorem 1 gives similar results to papers using descriptor system approach and bounding techniques from (Lee et al, 2004) and (Moon et al, 2001). Investigations to link all these results are developped in (Gouaisbaut and Peaucelle, 2006).…”

Sum-of-squares based observer design for polynomial systems with a known fixed time delay

“…If the matrix C has not the form assumed above but has full rank, then one can find a matrixC ∈ R (n−p)×n such that rank(C T ,C T ) = n and transform the states usingx = (C T ,C T ) T x. Hence, without loss of generality, the matrix C can be assumed to attain the form (19). …”

Robust Stability for a Class of Uncertain Singular Time-Delays Systems

“…One of the main purposes to analysize linear differential systems is to analyze the stability of the systems, especially the certain and uncertain linear differential control systems with time delay, which is important not only in theory but also in practice and arouses a lot of interests. Some results are obtained [1][2][3][4][5]. A delay-dependent criterion for determining the stability of systems with time-varying delays is obtained by combing a new approach for linear time delay systems based on a descriptor representation with a result on bounding of cross products of vectors in [1].…”

“…A delay-dependent criterion for determining the stability of systems with time-varying delays is obtained by combing a new approach for linear time delay systems based on a descriptor representation with a result on bounding of cross products of vectors in [1]. In [4], the system with single state delay and uncertainty is considered, and non-conservative results are obtained by using new Lyapunov-krasovskii functionals. The stability of regular systems with multiplestate delay and uncertainty is considered in [6], and based on Lyapunov-Krasovskii functionals combined with LMI techniques.…”