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

Abstract

SUMMARY This paper mainly studies the problem of the robustly stability analysis for uncertain neutral system with mixed time‐varying delays. By constructing an augmented Lyapunov–Krasovskii functional, some new delay‐dependent criteria can be established in terms of linear matrix inequalities. Compared with some existing results, our delay‐dependent criteria can be shown to be some less conservative ones via some illustrative numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.

Robust stabilization andH∞control of uncertain stochastic time-delay systems with nonlinear perturbation

“…By Lemma 3, the matrix inequalities (25) hold, if and only if there exist scalars " 1 > 0, " 2 > 0, such that the following matrix inequalities hold for i D 1; 2…”

A further note on stability criteria for uncertain neutral systems with mixed delays

“…Choose the same Lyapunov-Krasovskii functional (11), according to (20), the following equation holds [21]:…”

“…It is well known that the existence of time delay in a dynamical system often leads to the deterioration of system stability and performance. The stability criteria obtained in the literature can be divided into two categories: delay-independent [1][2][3][4][5][6][7][8][9][10][11][12][13] and delay-dependent criteria [14][15][16][17][18][19][20][21][22][23]. The delay-dependent results are less conservative than the delay-independent ones for taking advantage of additional information of the time delay.…”

“…Recently, the stability issue of neutral time-delay systems has been attracted many attentions and some valuable results are reported in [1][2][3][4][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and references therein. The practical examples of neutral delay-differential systems are found in the distributed networks containing lossless transmission lines [24], lossless transmission lines, partial element equivalent circuit [25] and population ecology [26], whose model is the time-delay systems of the neutral type and the delays are in both its state and the derivatives of the * Tel.…”

“…A new delay-dependent stability condition is derived in terms of linear matrix inequality to ensure a large upper bound of the time-delay by non-uniformly dividing the delay interval into multiple segments in [19]. By constructing an augmented Lyapunov-Krasovskii functional, some new delay-dependent criteria for an uncertain neutral system with mixed timevarying delays can be established in terms of linear matrix inequalities in [20]. Based on the Lyapunov stability theory and linear matrix inequalities (LMIs) method, the problem of robust stability for neutral type system with mixed delays and time-varying structured uncertainties is investigated in [21].…”