Delay‐dependent robust H_∞ control for uncertain stochastic time‐delay systems

Abstract

SUMMARYThis paper investigates the robust H ∞ control problem for stochastic systems with a delay in the state. Sufficient delaydependent conditions for the existence of state-feedback controllers are proposed to guarantee mean-square asymptotic stability as well as the prescribed H ∞ performance for the closed-loop systems. Moreover, the results are further extended to the stochastic time-delay systems with parameter uncertainties, which are assumed to be time-varying norm-bounded appearing in both the state and the input matrices. The appealing idea is to partition the delay, which differs greatly from the most existing results and reduces conservatism by thinning the delay partitioning. Numerical examples are provided to show the advantages of the proposed techniques.

Necessary and sufficient conditions of risk‐sensitive optimal control and differential games for stochastic differential delayed equations

“…We also note that, as in the nondelay case, the “completion of squares” method can be used for a class of linear‐quadratic (LQ) problems with the linear SDDE and the quadratic cost . Furthermore, the stabilization of the SDDE was considered by Song et al, and the LMI conditions for H ∞ control of the linear SDDE was identified by Yang et al The H ∞ control problem for the linear SDDE with perturbation was studied by Li and Yang …”

Effects of quantization and saturation on performance in bilateral teleoperator

“…Perhaps, the most interesting case is the use of Internet as a communication channel between the master and slave sites of a teleoperation system. However, this technology (Internet) presents problems for the development of control applications at distance . On the one hand, due to highly variable communication condition, such as congestion and channel quality, the transmission delay will cause poor tracking performance or even instability of teleoperation system.…”

Predictor Feedback Stabilization of Stochastic Linear Delayed Systems with Both Additive and Multiplicative Noises

“…To take these important factors into consideration, many real world applications have been modeled with stochastic delayed differential equations (SDDEs) [1]. By means of this method the stochastic system with input delay is transformed to a stochastic system with state delay and a wealth of excisting results on stabilization of state delayed stochastic systems can be utilized (see, for example, [7][8][9][10]). Static controllers are formed by using the state of the system multiplied by a constant gain matrix [2].…”