LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

Abstract

This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.

Robust Stochastic Sampled-Data H∞ Control for a Class of Mechanical Systems With Uncertainties

“…Theorem 1. Mechanical system (17) is asymptotically stable in mean square through feedback stochastic sampled-data control (12) with disturbance attenuation γ > 0, if there exist positive definite matricesP,…”

“…The problem of state estimation for phase-type semi-Markovian jump systems using sliding mode controller is discussed in [8]. Usually uncertainties are considered to be norm-bounded but since fractional uncertainties are more general than norm-bounded uncertainties, stability analysis of systems with linear fractional uncertainties has been carried out in the literature, see [9][10][11][12]. The problem of robust stability for neural networks with time-varying delays and parametric uncertainties has been investigated in [10].…”

“…The problem of robust stability for neural networks with time-varying delays and parametric uncertainties has been investigated in [10]. Delay-interval-dependent robust stability criteria for neutral stochastic neural networks and stochastic systems with polytopic and linear fractional uncertainties has been derived in [11,12], respectively.…”

Dynamical Behaviors of Stochastic Hopfield Neural Networks with Both Time-Varying and Continuously Distributed Delays

“…Many results on stochastic neural networks have been reported in . Some sufficient criteria on the stability of uncertain stochastic neural networks were derived in [4][5][6][7]. Almost sure exponential stability of stochastic neural networks was studied in [8][9][10].…”

Exponential Estimates of a Class of Time–Delay Nonlinear Systems with Convex Representations

“…In the TS context, the last decade has witnessed an abundance of results on a variety of issues related to time-delay systems: stability using the Lyapunov-Razumikhin functional approach (Cao and Frank, 2001), stability criteria for a class of nonlinear stochastic systems with time delay (Wang et al, 2004;Li et al, 2011;Balasubramaniam et al, 2012), design of feedback controllers design for nonlinear interval time-delay systems via a T-S model (Chang et al, 2004), design of guaranteed cost control for T-S systems with delays (Chen and Liu, 2005;Chen et al, 2007b;2007a;Kang and Wang, 2010) observer-based H-infinity control for time-delay T-S (Lin et al, 2007), α-dissipative control for T-S fuzzy descriptor systems with time delay (Gassaraa et al, 2014). Most of these results take advantage of the possibility of rewriting Lyapunov-Krasovskii functionals as convex expressions by inheritance of the model convex structure: this investigation follows that path.…”