Abstract
This paper is focused on the stabilization of Takagi–Sugeno fuzzy model-based Markovian jump systems with the aid of a delayed state observer. Due to network-induced constraints in the communication channel, a delay partition method combined with an event-triggered mechanism is proposed to design the observer. Then, a novel integral sliding surface is designed, based on which sliding mode dynamics is obtained. Further, according to stochastic stability theory, feasible conditions are provided to ensure the sliding mode dynamics and the error dynamics have an H∞ attenuate level γ. The challenge is to deal with the issue that transition rates may be totally unknown. Moreover, an observer-based sliding mode controller is constructed to ensure the finite-time reachability of the predefined sliding surface. Finally, a numerical example based on a robotic manipulator is given to verify the effectiveness of the proposed method.
Highlights
With the strong demands for modeling a physical system with high accuracy, for instance, the physical systems may have structural mutation due to changes of power, the shift of parameters and external disturbances, etc., which provoke the need to seek for more suitable mathematical models
With matched/unmatched uncertainties based on the T-S fuzzy model was studied in [17]; the robust H∞ control involving a class of uncertain stochastic Markovian jump systems (MJSs) was investigated in [18], etc. [19,20,21]
The signal is transmitted in the output channel of observer that may suffer from network-induced delays, where the output measurement y(t) sampled periodically with sampling period T
Summary
With the strong demands for modeling a physical system with high accuracy, for instance, the physical systems may have structural mutation due to changes of power, the shift of parameters and external disturbances, etc., which provoke the need to seek for more suitable mathematical models. The researches on MJSs have been reported by many in both applications and theoretical aspects, such as the Markov jump models are widely applied in nuclear power systems, manufactory and network communication [2,3,4,5], etc It witnessed the issue of stochastic stability analysis, stabilization, filter design and so on. The main contributions of this paper can be concluded as: (1) Compared with traditional observer, the proposed event-triggered time-delay state observer brings the benefits that error is better suppressed and better stabilization property is obtained; (2) a novel sliding surface function is proposed, based on which the observer gain matrices can be computed in the design process rather than given as in [42]; (3) a new method is proposed to give feasible strict LMI conditions for stability of MJSs with totally unknown transition information; and (4) fuzzy SMC law ensures.
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