Abstract
This paper deals with the problem of mixed H2/H∞ control for Itô-type stochastic time-delay systems. First, the H2/H∞ control problem for stochastic time-delay systems is presented, which considers the mean square stability, H2 control performance index, and the ability of disturbance attenuation of the closed-loop systems. Second, by choosing an appropriate Lyapunov–Krasoviskii functional and using matrix inequality technique, some sufficient conditions for the existence of state feedback H2/H∞ controller for stochastic time-delay systems are obtained in the form of linear matrix inequalities. Third, two convex optimization problems with linear matrix inequality constraints are formulated to design the optimal mixed H2/H∞ controller which minimizes the guaranteed cost of the closed-loop systems with known and unknown initial functions, and the corresponding algorithm is given to optimize H2/H∞ performance index. Finally, a numerical example is employed to show the effectiveness and feasibility of the proposed method.
Highlights
There has been a rapid increase of interest in the study of stochastic systems due to the importance of stochastic models in science and engineering, such as finance systems [1] and power systems [2]
The problem of guaranteed cost robust stable control was considered via state feedback for a class of uncertain stochastic systems with time-varying delay in [6]
In [19], the problem of nonfragile observer-based H∞ control for stochastic timedelay systems was considered. e problems of robust stabilization and robust H∞ control with maximal decay rate were investigated for discrete-time stochastic systems with time-varying norm-bounded parameter uncertainties in [20]
Summary
There has been a rapid increase of interest in the study of stochastic systems due to the importance of stochastic models in science and engineering, such as finance systems [1] and power systems [2]. E finite-time tracking control of a class of stochastic quantized nonlinear systems was studied in [5]. The problem of guaranteed cost robust stable control was considered via state feedback for a class of uncertain stochastic systems with time-varying delay in [6]. Gao et al [12] investigated the problem of H2/H∞ control for nonlinear stochastic systems with time-delay and state-dependent noise. Motivated by the abovementioned discussions, in this work, we aim to investigate the mixed H2/H∞ control for Ito-type stochastic time-delay systems. (i) e definition of H2/H∞ control for Itotype stochastic time-delay systems is presented, which considers stability, H2 control performance index, and H∞ control performance index. Notations: A′ denotes the transpose of matrix A; tr(A) indicates the trace of matrix A; A > 0(A ≥ 0) indicates that A is a positive definite (positive semidefinite) matrix; In×n represents a n-dimensional identity matrix; Rn shows n-dimensional Euclidean space; E represents the mathematical expectation of random process; and the asterisk “∗” in the matrix indicates symmetry term
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
