Abstract
This paper develops a new observer-based sliding mode control (SMC) scheme for a general class of Ito^ stochastic delay systems (SDS). The key merit of the presented scheme lies in its simplicity and integrity in design process of the traditional sliding mode observer (SMO) strategy, i.e., the state observer and sliding surface design as well as the associated sliding mode controller synthesis. For guaranteeing to use the scheme, a new LMIs-based criterion is established to ensure the exponential stability of the underlying sliding mode dynamics (SMDs) in mean-square sense with H∞ performance. A bench test example is provided to numerically demonstrate the efficacy of the scheme and illustrate the application procedure for potential readers/users with interest in their ad hoc applications and methodology expansion.
Highlights
It has been widely witnessed that control of stochastic systems has increasingly received much attention as one of the most practically meaningful systems in both academic research and application fields [1]
The associated control design problems have been explored for the systems in parallel with the development of system control theory, e.g., H∞ control and filtering [4,5,6]
Some representative results regarding the sliding mode control (SMC) of stochastic delay systems (SDS) include SMC of uncertain SDS [14], SMC for uncertain SDS with H∞ performance index [15] to deal with a limitation (i.e., there exist a matrix G with appropriate dimension satisfying Gg(t, x(t), x(t − d)) = 0 for all t ≥ 0); further, robust SMC of uncertain SDS has been considered where such restrictive condition to the most existing results is removed in [16]
Summary
It has been widely witnessed that control of stochastic systems has increasingly received much attention as one of the most practically meaningful systems in both academic research and application fields [1]. In view of a new observer-based SMC design, a class of nonlinear delay systems was investigated in [25], and recently in [26] robust H∞ control for uncertain singular time-delay systems was studied via a novel SMO synthesis. To the best of the authors’ knowledge, vast majority of the existing routes for the SMO are that: state observer is designed to generate the original state with assistance of the control input and/or its compensator to restrain the uncertainties and nonlinearity of the system and make the closed-loop systems operate stably. An improved procedure is created from the fact that if the stability of the original system and its error system can be ensured, the observer state can tend to be stable as it is All these features distinguish the present scheme from the existing literatures.
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