Robust Stability Of Stochastic Systems Research Articles

Robust stability of stochastic systems with varying delays: Application to RLC circuit with intermittent closed-loop

This paper characterizes the robust second-moment stability of stochastic linear systems subject to varying delays. The delays assume a particular form suitable to represent packet loss in networked control systems, under the zero-order hold feedback. The proposed robust stability condition requires checking the spectral radius of an appropriate matrix that that depends on uncertain parameters belonging to a polytope. Due to this polytope’s dependence, checking the spectral radius is difficult from the numerical viewpoint. As an attempt to solve the problem, we convert the polytope-based condition into a randomized approach. Namely, we present probability bounds that help us certificate the robust second-moment stability under high probability. A real-time electronic application illustrates the potential benefits of our approach.

On Robust Stability of Stochastic Systems with Uncertainties and Distributed Time-Varying Delays

This paper is concerned with the robust stability analysis for uncertain stochastic systems with distributed time-varying delays. By using the stochastic analysis approach and free-weighting matrices, new delay-dependent stability condition is established in terms of LMI to guarantee the uncertain stochastic distributed delay system to be robustly asymptotically stable in the mean square.

Robust Stabilization of Uncertain Stochastic Systems with Delay in Control Input

This paper discusses the problems of robust stabilization of stochastic systems with parametric uncertainties and time delay in control input. The parametric uncertainties which appear in all system matrices are assumed to be norm bounded. The delay-dependent stabilization condition is derived by taking the relationships between terms in the Leibniz-Newton formula into account. Free-weighting matrices are employed to express these relationship, and the sufficient stabilization condition is formulated in terms of linear matrix inequality (LMI) based on the Lyapunov-Krasovskii theory, which can be solved by LMI toolbox in Matlab

Robust Stabilization for Stochastic Systems with Time‐Delay and Nonlinear Uncertainties

This paper deals with the problem of robust stabilization of stochastic systems with time‐delay and nonlinear uncertainties via memory state feedback. Based on Lyapunov krasoviskii functional, some sufficient conditions on local (global) stabilization are given in terms of matrix inequalities. In particular, these stabilizable conditions for a class of nonlinear stochastic time‐delay systems are derived in the form of linear matrix inequalities, which have the advantage of easy computation. Moreover, the corresponding results are further extended to the stochastic multiple time‐delays systems. Finally, an example is presented to show the superiority of memory state feedback controller to memoryless state feedback controller.

The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters

The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov-Krasovskii functional and employing the decomposition technique of interval matrix and Ito’s formula, the delay-dependent criteria for the p-moment exponential robust stability are obtained. Numerical examples show the validity and practicality of the presented criteria.

Robust stabilization of stochastic systems based on the LQ controller

The robust exponential stability in mean square for a class of linear stochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we have designed an optimal controller which guarantees the exponential stability of the system. Actually, we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to have shown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria for the exponential stability on the linear stochastic uncertain closed-loop systems are given.

Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties

The authors are concerned with delay-dependent stability for a class of stochastic systems with time delay and nonlinear uncertainties. A stability criterion, expressed in terms of LMI, is derived based on the Lyapunov-Krasovskii function method and a parameterised model transformation. An example shows that the proposed method is less conservative than alternative methods.