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A Relaxed Observer-based Control for LPV Stochastic Systems Subject to H∞ Performance

Cheung-Chieh Ku* and Guan-Wei Chen
International Journal of Control, Automation, and Systems, vol. 18, no. 4, pp.1033-1044, 2020

Abstract : A relaxed observer-based control problem of the disturbed Linear Parameter Varying (LPV) stochastic systems is addressed in this paper. For the control problem, some sufficient conditions are derived via a Lyapunov function whose positive definite matrix is not required as the diagonal case. Besides, a general H∞ performance index is proposed to constrain the effect of external disturbance on the state and estimation error. Furthermore, a lemma is proposed to eliminate the oscillation caused by determining performance level of state and estimation error. Another lemma is developed via extending projection lemma to convert the derived conditions into strict Linear Matrix Inequality (LMI) form. By using convex optimization algorithm, all feasible solutions can be obtained by a single-step calculation to establish an observer-based Gain-Scheduled (GS) controller. Based on the designed controller, the asymptotical stability and H∞ performance of the LPV stochastic systems can be guaranteed in the sense of mean square. Finally, two examples are provided to demonstrate the effectiveness and applicability of the proposed method.

Keyword : Gain scheduled control, H∞ performance, LPV system, multiplicative noise, observer-based control.

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