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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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徐胜元, Shengyuan Xu, Paul Van Dooren, Radu Stefan, James Lam
IEEE TRANSACTIONS ON AUTOMATIC CONTROL VOL.47 NO.7(2002)1122-1128,-0001,():
-1年11月30日
This note considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties,while the purpose of robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method.
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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】Robust H∞ Filtering for Uncertain 2-D Continuous Systems
徐胜元, Shengyuan Xu, James Lam, Senior Member, IEEE, Yun Zou, Zhiping Lin, and Wojciech Paszke
IEEE TRANSACTIONS ON SIGNAL PROCESSING VOL.53 NO.5(2005)1731-1738,-0001,():
-1年11月30日
This paper considers the problem of robust H∞ filtering for uncertain two-dimensional (2-D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The purpose is the design of a 2-D continuous filter such that for all admissible uncertainties, the error system is asymptotically stable, and the H∞ norm of the transfer function, from the noise signal to the estimation error, is below a prespecified level. A sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H∞ filter is given. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method
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徐胜元, Shengyuan Xu, James Lam
IEEE TRANSACTIONS ON FUZZY SYSTEMS VOL.13 NO.1(2005)82-93,-0001,():
-1年11月30日
This paper investigates the problem of robust output feedback H∞ control for a class of uncertain discrete-time fuzzy systems with time delays. The state-space Takagi–Sugeno fuzzy model with time delays and norm-bounded parameter uncertainties is adopted. The purpose is the design of a full-order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed-loop system and guarantees an H∞ norm bound constraint on disturbance attenuation for all admissible uncertainties. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of this problem is presented. Explicit expressions of a desired output feedback controller are proposed when the given LMIs are feasible. The effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust H∞ control for a class of uncertain nonlinear discrete delay systems.
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