Delay-dependent condition for absolute stability of Lurie control systems with multiple time delays and nonlinearities

Abstract

The absolute stability of Lurie system with multiple time delays and nonlinearities is considered in this paper. Based on the Lyapunov stability theory, using the descriptor system approach and the method of decomposing matrices, a novel delay-dependent sufficient condition for the absolute stability of Lurie system is derived and expressed in the form of the linear matrix inequality (LMI). The maximum upper bound of the allowable delay is obtained by solving a convex optimization problem. A numerical example shows that the result obtained in this paper improved the estimate of the stability limit over some existing results.

Further improvement on delay-range-dependent robust absolute stability for Lur׳e uncertain systems with interval time-varying delays

“…The Lur'e system is one of a significant class of nonlinear systems and has a nonlinear element satisfying certain sector bounded constraints. Since the Lur'e system and absolute stability were firstly introduced by [26,27], the study of the absolute stability for Lur'e system has attracted many researchers [2,[3][4][5][6][9][10][11][12]14,15,19,20,25,[28][29][30][32][33][34][35][36][39][40][41][42]. Also, in practice, the systems almost present some uncertainties because it is very difficult to obtain an exact mathematical model due to environmental noise, uncertain or slowly varying parameters.…”

“…The problem of absolute stability of Lur'e system has received considerable attention in the control community, and many valuable results, such as Popov criterion, Circle criterion, and Kalman-Yakubovih-Popov lemma have been reported [21]. As time-delays are frequently encountered in practical systems and are often a source of instability and poor performance, the problem of absolute stability of Lur'e systems with time-delay has been attracting much attention [2,[3][4][5][6][9][10][11][12]19,20,25,[28][29][30][33][34][35][36]41,42]. In stability analysis of system with time delays, delay-dependent methods [3][4][5][6][10][11][12]20,25,[28][29][30][33][34][35][36]41,42] have been paid more attentions than delay-independent one [2,9,19] because of the fact that the sufficient conditions with delaydependent method provide maximum delay bounds for guaranteeing the asymptotic stability of the concerned system and are generally less conservative than delay-independent ones.…”

The Delay-Dependent Condition for T-S Fuzzy Lurie Control Systems with Multiple Time-Delays

“…In addition, several novel delay-dependent conditions for absolute stability of Lurie systems with multiple time-delays have been derived [6,7] based on the Linear matrix inequality (LMI) approach. The advantage of this method is that it uses free weighting matrices to express those relationships.…”

The Delay-dependent Condition for Uncertain T-S Fuzzy Lurie Control Systems with Time-delay

“…But the stability conditions mentioned above are all delay-independent, which are often conservative when time-delay is small. Based on this, a considerable number of delay-dependent absolute stability conditions have been proposed [3]. Moreover, since Lurie direct type control systems include a class of plants without any practicality in engineering practice, some delay-dependent stability conditions have also been proposed in [4,5] for uncertain Lurie indirect systems.…”