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In this paper, the problem of simultaneous fault detection and control for continuous-time switched state-delay systems under asynchronous switching is investigated. The aim is to design a detector/controller unit where the detector is an observer and the controller is an observer-based controller. Based on the average dwell time approach, a new method is proposed where both stability and fault detection are considered, simultaneously, through certain performance indexes. This problem is formulated as a mixed H∞/ H− problem and its solution leads to new sufficient conditions in the form of linear matrix inequality feasibility conditions. The effectiveness of the design technique is illustrated via an example.

This study presents a general control law based on Lyapunov’s direct method for a group of well-known stochastic chaotic systems. Since real chaotic systems have undesired random-like behaviors which have also been deteriorated by environmental noise, chaotic systems are modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of Wiener process which eventually generates an Ito differential equation. Proposed controller not only can asymptotically stabilize these systems in mean-square sense against their undesired intrinsic properties, but also exhibits good transient response. Simulation results highlight effectiveness and feasibility of proposed controller in outperforming stochastic chaotic systems.