Chapter 6Robust H2 Sliding Mode Control

In the past two decades, the sliding mode control (SMC) problem of continuous-time systems has been extensively studied and the corresponding results have been widely applied in various fields, due primarily to the strong robustness of the sliding motion on the sliding surface against model uncertainties, parameter variations, and external disturbances. Since most control strategies are implemented digitally, the SMC problem in the discrete-time setting has recently started to gain some research interests and a number of results have been reported in the literature.

On the other hand, as it is now well recognized that stochastic systems are suitable to be used to model physical systems, financial systems, ecological systems, as well as social systems, the stochastic control problem has drawn much research attention and many analysis as well as synthesis methodologies have been developed. In recent years, the SMC problem for stochastic systems has stirred considerable research interests and a series of papers have been published. However, it should be pointed out that the existing literature on the discrete-time SMC problem has been concerned with deterministic linear systems with or without matched nonlinear disturbances. In terms of the importance of both the discrete-time system and stochastic system in practice, it seems quite promising to investigate the SMC method for discrete stochastic systems. Unfortunately, up to now, the SMC ...

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