An augmented model for robust stability analysis of time-varying delay systems

Abstract

Stability analysis of linear systems with time-varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modeling of the delay system. New types of Lyapunov Krasovskii functionals are then proposed allowing to reduce the conservatism of the stability criterion. Delay dependent stability conditions are then formulated in terms of linear matrix inequalities (LMI). Finally, several examples show the effectiveness of the proposed methodology.

Augmented Lyapunov–Krasovskii functional approaches to robust stability criteria for uncertain Takagi–Sugeno fuzzy systems with time-varying delays

“…Therefore, our proposed stability criteria are derived in the form of (ii) in Lemma 1. Furthermore, inspired by the work of [17][18][19][20], our approach utilized the triple integral forms of Lyapunov-Krasovskii's functional. However, unlike the method of [20], different upper bound ofV 7 was taken to utilize more information about h(t) as mentioned in Remark 1, which may lead to less conservative results.…”

“…First, by constructing an augmented Lyapunov-Krasovskii functional and utilizing Finsler's lemma, a delay-dependent stability condition without the use of free weighting matrices is derived in terms of LMIs, which will be introduced in Theorem 1. Inspired by the works of [17][18][19][20], a triple integral form of Lyapunov-Krasovskii functional is utilized. Also, new integral forms of states (…”

On the reachable set bounding of uncertain dynamic systems with time-varying delays and disturbances

“…Thus, extensive researches on the delay-dependent stability or stabilization criteria for dynamic systems with time-delay, which give the available information about the maximum allowable time-delay required to guarantee stability, have been conducted by many researchers during the last decade. An overview and recent survey in this field can be obtained from [1,[8][9][10][11]13,14] and the references therein. Recently, new Lyapunov-Krasovskii's functionals of the form of triple integrals were proposed in [1], and their stability conditions showed an improvement in the maximum delay bound which is an important index for checking of the conservatism of the delay-dependent stability criteria.…”

Stability of systems with fast-varying delay using improved Wirtinger's inequality

“…Another technique is based on the construction of Lyapunov-Krasovskii functionals (see for instance [5] in order to apply extension of Lyapunov theory to the case of delay systems. The construction of these functionals often induces an important conservatism and several attempts have been proposed to reduce it by choosing extended state based Lyapunov-Krasovskii functionals ( [1], [13]), or discretized Lyapunov functionals ( [8]). The third step which brings an important source of conservatism comes from the inequalities to be used to derive a tractable numerical optimization problem (see [10], [11], [14], [17], [21], [23].…”