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

This paper considers the stability and L-2-L-infinity control problem for Ito 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 stochastic noises is investigated. For the delayed stochastic system without the disturbance, an 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-infinity, 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.

Automated summary

This paper investigates the stability and control problem of Ito stochastic systems with sawtooth-like input delay. A new auxiliary system is introduced to reduce the conservatism of the system, and the influence of stochastic noises is considered. The stability criterion and controller design method are derived using stochastic inequalities and modified polynomial inequalities. Furthermore, a new augmented Lyapunov-Krasovskii functional is proposed to increase the terms in the discriminant. Two numerical examples are provided to demonstrate the validity and effectiveness of the theoretical results.