New Results on the Stability and L₂-L∞ Control of Itô Stochastic Systems With Sawtooth-Like Input Delay

Abstract

This paper considers the stability and L 2 -L ∞ control problem for Itô stochastic systems with the sawtooth-like input delay. Compared with previously-known results on systems with the sawtooth-like input delay, a new auxiliary system is introduced to reduce the conservatism of the system. Besides, the influence of the stochastic noises is investigated. For the delayed stochastic system without the disturbance, a LMI type mean-square asymptotical stability criterion is derived by using the Bessel-Legendre stochastic inequality and a modified finite-interval quadratic polynomial inequality. Then a linear feedback controller is proposed to realize the stability of the system with a prescribed L 2 -L ∞ performance under the influence of disturbances, where the controller gain matrix is designed by introducing slack variables. To be pointed out that the augmented Lyapunov-Krasovskii functional (LKF) used in this paper is new, which is constructed by introducing an auxiliary system to increase the delay-dependent function terms in the discriminant. Finally, two numerical examples are given to show the validness and effectiveness of the theoretical results.INDEX TERMS Itô stochastic system, Sawtooth-like input delay, Mean-square asymptotical stability, L 2 -L ∞ control, Quadratic polynomial inequality

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