SUMMARYThis paper studies the input‐to‐state stability (ISS) of descriptor systems with exogenous disturbances. on the basis of the ISS theory of standard state‐space nonlinear systems, a sufficient condition for a class of nonlinear descriptor system to be ISS is proved. Furthermore, a design method of the state feedback controllers is given to make the closed‐loop system ISS. A numerical example is given to illustrate the effectiveness of the controller design.Copyright © 2012 John Wiley & Sons, Ltd.

In this article, the [Formula: see text] control problem of a class of singular Markov jump systems with time-varying inputs and state delays is investigated. Based on the Lyapunov stability theory, by constructing a different Lyapunov–Krasovskii functional, the sufficient conditions of being stochastic stable and having H∞ performance index are given. Then, the design method of state feedback controller is given to ensure the closed-loop system is stochastic stable and has [Formula: see text] performance index. Finally, simulation examples are given to verify the effectiveness of the proposed methods.

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