Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations

Abstract

a b s t r a c tThis paper considers the problem of robust stability of neutral systems with mixed timevarying delays and nonlinear perturbations. Two type uncertainties such as nonlinear time-varying parameter perturbations and norm-bounded uncertainties have been discussed. Based on the new Lyapunov-Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities (LMIs). Finally, four numerical examples are given to illustrate the effectiveness and an improvement over some existing results in the literature with the proposed results.

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

“…It is well known that time-delays can cause poor performance or instability. Therefore, the problem of delay-dependent stability and stabilization for T-S fuzzy systems with time-delays has been received great efforts by many researchers in recent years [2,[4][5][6][7][8][9][10][11][12][13] because delay-dependent approaches are generally less conservative than delay-independent ones when the sizes of time-delays are small [14].…”

New criteria on stability analysis for uncertain neutral system with mixed time‐varying delays

“…So, Theorem is more effective than the ones in . Besides, our result can also extend to deal with the robust stability for neutral system with mixed time‐varying delay and nonlinear perturbations . Here, we omit it.…”

“…However, the foregoing stability criteria for neutral system with time‐varying delay are only applicable to the case when the lower bound of the delay is zero. Recently, delay‐dependent stability for linear system with interval time‐varying delay was investigated in . In , Yu and Lien have obtained the robust stability criteria for uncertain neutral systems with interval time‐varying delay by the free‐weighting matrices, but these criteria are neutral‐delay‐independent.…”

“…With the descriptor model transformation and the decomposition technique of discrete‐delay term matrix, Kwon, et al have studied the robust stability analysis for uncertain neutral systems with interval time‐varying delay, and their obtained stability criteria are independent of the neutral delay. Although some linear matrix inequality (LMI)‐based sufficient conditions ensuring the robust stability for neutral systems with mixed time‐varying delay and nonlinear perturbations have been obtained in by constructing an augmented Lyapunov–Krasovskii functional which contains some triples terms, these conditions are gained by replying on the bounding technique. As we know, the mode transformation, the bounding technique, and the approaches of decomposing the matrix usually brings conservatism to the stability criterion.…”

Singular Distributed Parameter System Iterative Learning Control with Forgetting Factor with Time- Delay

“…Time-delay occurs in various physical, industrial and engineering systems such as biological systems, neural networks, networked control systems, multi-agent systems, and so on [5][6]. It is well known that the existence of timedelay is source of proof performance and instability of dynamic systems [7][8].…”