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This article considers the finite-time H ∞ control problem for singular Markovian jump systems with time-varying delay subject to input saturation. Considering the discontinuities caused by the mode-dependent singular matrix and Markovian jump switching behavior, the result of this article is more practical. First, a hidden model-based state feedback controller is designed to guarantee that the considered system is mean-square locally finite-time H ∞ stabilizable by employing an appropriate Lyapunov function. Second, some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities which considers the time-varying delay and input saturation. Finally, the correctness of the proposed method is verified by three numerical examples. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finite-time robust decentralized control for uncertain continuous-time singular large-scale systems with exogenous disturbances (UCSLSSED). The concept of finite-time robust decentralized stabilization for UCSLSSED is introduced by definition of finite-time stability for uncertain continuous-time large-scale systems with exogenous disturbances. The analyses of finite-time robust bounded and finite-time robust stabilization for UCSLSSED are done. The design approach of finite-time robust decentralized state feedback controller is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

SUMMARY This paper discusses the exponential stability and stabilization for nonlinear descriptor systems with discrete and distributed delays. In terms of the Lyapunov method, the exponential stability of the slow subsystem is firstly obtained. Then, a new homotopy-based approach is proposed to investigate the exponential stability of the fast subsystem. By an estimate of the weighted matrix norm for a nonlinear mapping, the exponential stability of the fast subsystem and thus delay-dependent sufficient conditions for the exponential stability of the systems are obtained. In addition, a state feedback controller is designed for the stabilization of the nonlinear descriptor systems. Finally, the effectiveness of the proposed approach is illustrated by numerical examples. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]