Finite-Time H_∞ Control for Itô-Type Nonlinear Time-Delay Stochastic Systems

Abstract

The finite-time H ∞ control problem for an Itô-type stochastic system with nonlinear perturbation and time delay is investigated. First, the finite-time H ∞ control problem for a nonlinear time-delay stochastic system is presented taking into consideration both the transient performance and the capability to attenuate the disturbance of a closed-loop system in a given finite-time interval. Second, using the Lyapunov-Krasoviskii functional method and the matrix inequality technique, some sufficient conditions for the existence of finite-time H ∞ state feedback controller and dynamic-output feedback controller for nonlinear time-delay stochastic systems are obtained. These conditions guarantee the mean-square finitetime bounded-ness of the closed-loop systems and determine the H ∞ control performance index. Third, this problem is transformed into an optimization problem with matrix inequality constraints, and the corresponding algorithms are given to optimize the H ∞ performance index and obtain the maximum timedelay. Finally, a numerical example is used to illustrate the effectiveness of the proposed method. INDEX TERMS Stochastic systems, nonlinear perturbations, finite-time stability, H ∞ control, time-delay.

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

“…In this section, we use the LMI parser YALMIP and the SDP solver Sedumi in MATLAB to get our results. Inspired by [36], we propose two algorithms: one finds the maximum value of h M , the other finds the minimum values of γ and K. 7),( 8),( 17),(18) γ 2 . Step 4: Let i = i + 1, if i+1>n, move to Step 5; otherwise, return to Step 3.…”

Finite‐time stable of time‐varying delay distributed parameter systems with input saturation via periodically intermittent control

“…The concept of finite-time stability has also been extended to robust stability control, 25 fault-tolerant control, 26 and H-infinity control. 27,28 At present, rich research results have been obtained for the finite-time synchronization control of complex systems and multiple agents. [20][21][22][29][30][31][32][33][34][35][36] For example, in paper, 30 the finite-time synchronization problem of a class of coupled complex partial differential systems was studied; in paper, 20 the finite-time synchronization problem of switched neural networks with state-dependent switching under intermittent control was discussed; in paper, 35 the robust guaranteed cost finite time control problem of coupled neural networks with parameter uncertainties was studied, and the robust guaranteed cost control law included continuous feedback controller and intermittent feedback controller.…”

Finite-Time Annular Domain Bounded Control of Itô-Type Stochastic Systems With Wiener and Poisson Random Disturbance

“…Fortunately, the concept of finite-time stability (FTS) is put forward [30]. Due to the advantage of the finite-time technique, there have been many nice results on it, such as the FTS of switched stochastic systems [31]- [33], FTS of stochastic delayed systems [34]- [36], FTS of stochastic Markovian jump systems [37], [38]. Besides, external disturbance is unavoidable in practice.…”