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【期刊论文】Robust H∞ Filtering for Uncertain Markovian Jump Systems With Mode-Dependent Time Delays
徐胜元, Shengyuan Xu, Tongwen Chen, James Lam
IEEE TRANSACTIONS ON AUTOMATIC CONTROL VOL.48 NO.5(2003)900-907,-0001,():
-1年11月30日
This note considers the problem of robust H∞ filtering for uncertain Markovian jump linear systems with time-delays which are timevarying and depend on the system mode. The parameter uncertainties are time-varying norm-bounded. The aim of this problem is to design a Markovian jump linear filter that ensures robust exponential mean-square stability of the filtering error system and a prescribed L2-induced gain from the noise signals to the estimation error, for all admissible uncertainties. A sufficient condition for the solvability of this problem is obtained. The desired filter can be constructed by solving a set of linear matrix inequalities. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.
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【期刊论文】Reduced-Order H∞ Filtering for Stochastic Systems
徐胜元, Shengyuan Xu, Tongwen Chen
IEEE TRANSACTIONS ON SIGNAL PROCESSING VOL.50 NO.12(2002)2998-3007,-0001,():
-1年11月30日
This paper deals with the reduced-order H∞ filtering problem for stochastic systems. Necessary and sufficient conditions are obtained for the existence of solutions to the continuous-time and discrete-time problems in terms of certain linear matrix inequalities (LMIs) and a coupling nonconvex rank constraint condition. Furthermore, when these conditions are feasible, an explicit parametrization of all desired reduced-order filters corresponding to a feasible solution is given. In particular, when the reduced-order filter is restricted to be a static one, then simple conditions expressed by LMIs only without any rank constraints are derived, and a parametrization of all solutions is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed approach.
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徐胜元, Shengyuan Xu, James Lam, Senior Member, IEEE
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS VOL.51 NO.9(2004)1897-1905,-0001,():
-1年11月30日
This paper deals with the problems of positive real (PR) analysis and PR control for uncertain discrete-time descriptor systems. The parameter uncertainties are assumed to be time-invariant norm bounded and appear in both the state and input matrices. A new necessary and sufficient condition for a discrete-time descriptor system to be regular, causal, stable and extended strictly PR (ESPR) is proposed in terms of a strict linear matrix inequality. Based on this, the concepts of strong robust admissibility with ESPR and strong robust admissibilizability with ESPR were introduced. Without any additional assumptions on the system matrices, necessary and sufficient conditions for strong robust admissibility with ESPR and strong robust admissibilizability with ESPR are obtained. Through these results, the problems of PR analysis and PR control are solved. Furthermore, an explicit expression of a desired state feedback controller is also given, which involves no decomposition of the system matrices.
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【期刊论文】 H∞ Filtering for Singular Systems
徐胜元, Shengyuan Xu, James Lam, Yun Zou
IEEE TRANSACTIONS ON AUTOMATIC CONTROL VOL.48 NO.12(2003)2217-2222,-0001,():
-1年11月30日
This note considers the H∞ filtering problem for linear continuous singular systems. The purpose is the design of a linear filter such that the resulting error system is regular, impulse-free and stable while the closed-loop transfer function from the disturbance to the filtering error output satisfies a prescribed H∞-norm bound constraint.Without decomposing the original system matrices, a necessary and sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. Finally, an illustrative example is presented to demonstrate the applicability of the proposed approach.
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徐胜元, Shengyuan Xu, James Lam
IEEE TRANSACTIONS ON AUTOMATIC CONTROL VOL.49 NO.4(2004)568-574,-0001,():
-1年11月30日
This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively.With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.
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