Robust Exponential Stability and Stabilization of a Class of Nonlinear Stochastic Time‐Delay Systems

Abstract

This paper presents new exponential stability and delayed-state-feedback stabilization criteria for a class of nonlinear uncertain stochastic time-delay systems. By choosing the delay fraction number as two, applying the Jensen inequality to every sub-interval of the time delay interval and avoiding using any free weighting matrix, the method proposed can reduce the computational complexity and conservativeness of results. Based on Lyapunov stability theory, exponential stability and delayed-state-feedback stabilization conditions of nonlinear uncertain stochastic systems with the state delay are obtained. In the sequence, the delayed-state-feedback stabilization problem for a nonlinear uncertain stochastic time-delay system is investigated and some sufficient conditions are given in the form of nonlinear inequalities. In order to solve the nonlinear problem, a cone complementarity linearization algorithm is offered. Mathematical and/or numerical comparisons between the proposed method and existing ones are demonstrated, which show the effectiveness and less conservativeness of the proposed method.

Further studies on robust H∞ control for a class of Takagi–Sugeno fuzzy time-delay systems with application to continuously stirred tank reactor problems

“…If the LMIs (equations (17) and 25 Remark 5. In contrast to the classical CCL algorithms given in Li et al, 47 the stopping criterion of recursive algorithms in Step 4 has been modified, which can be detected effectively.…”

Model‐Reference Adaptive Moment Control of Uncertain Nonlinear Stochastic Systems

“… studied the problems of stabilization of uncertain singular Markovian jump systems with dependent noise and nonlinear stochastic systems with no unforced dynamics respectively. presented exponential stability and delayed‐state‐feedback stabilization criteria for a class of nonlinear uncertain stochastic time‐delay systems. investigated a design method for robust nonfragile PID control that is based on the guaranteed cost control problem for a class of uncertain discrete‐time stochastic systems with additive gain perturbations.…”

Robust Stability Analysis for Systems with Time‐Varying Delays: A Delay Function Approach

“…Zhang [34] and Zhao [35] considered a two term approximation of time delay for stability analysis. The delay decomposition method [36][37][38][39] has also been used extensively.…”