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Erschienen in:
2015 | OriginalPaper | Buchkapitel
6. Sliding Mode Control with Time-Varying Delays and Randomly Occurring Nonlinearities
verfasst von : Jun Hu, Zidong Wang, Huijun Gao
Erschienen in: Nonlinear Stochastic Systems with Network-Induced Phenomena
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Abstract
In this chapter, the robust sliding mode control (SMC) problem is firstly investigated for a class of uncertain discrete stochastic systems with randomly occurring nonlinearities (RONs) and time delays. The RONs, which describe the phenomena of a class of nonlinear disturbances occurring in a random way, are modeled according to a Bernoulli distributed white sequence with a known conditional probability. Sufficient conditions are derived to ensure the stability of the sliding mode dynamics under the specified sliding surface. Such conditions are characterized in terms of a set of linear matrix inequalities with an equality constraint. A discrete-time SMC law is synthesized to guarantee the reaching condition of the discrete sliding mode surface. A computational algorithm is introduced to facilitate the implementation of the proposed control strategy. Moreover, the robust \(H_\infty \) SMC problem is investigated for a general class of discrete uncertain systems with stochastic nonlinearities and time-varying delays.