Positive Real Control for Uncertain Singular Time-delay Systems via Output Feedback Controllers

This paper deals with the problem of positive real control for continuous singular systems with time delays and norm-bounded parameter uncertainties. The problem we address here is the design of an output feedback controller such that the resulting closed-loop system is regular, impulse-free and stable, while the closed-loop transfer function from the disturbance to the controlled output is extended strictly positive real for all admissible uncertainties. A sufficient condition for the solvability of this problem is obtained and a linear matrix inequality approach is developed. In addition, an explicit expression for the construction of a desired output feedback controller is given. An illustrative example is provided to demonstrate the effectiveness and applicability of the proposed approach.

[1]  Lihua Xie,et al.  Positive real analysis and synthesis of uncertain discrete time systems , 2000 .

[2]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[3]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[4]  Anuradha M. Annaswamy,et al.  An adaptive Smith-controller for time-delay systems with relative degree n*≤2 , 2003, Syst. Control. Lett..

[5]  Shengyuan Xu,et al.  On positive realness of descriptor systems , 2002 .

[6]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[7]  F. Lewis.  A survey of linear singular systems , 1986 .

[8]  Izumi Masubuchi,et al.  PII: S0005-1098(96)00193-8 , 2003 .

[9]  L. Xie,et al.  Robust H^∞ Control for Linear Systems with Norm-Bounded Time-Varying Uncertainty , 1990 .

[10]  Shengyuan Xu,et al.  H∞ and positive-real control for linear neutral delay systems , 2001, IEEE Trans. Autom. Control..

[11]  D. Bernstein,et al.  Robust stabilization with positive real uncertainty: beyond the small gain theory , 1991 .

[12]  J. Geromel,et al.  On strict positive real systems design: guaranteed cost and robustness issues 1 1 This research was , 1999 .

[13]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[14]  Magdi S. Mahmoud.  Discussion on: "Positive Real Control for Uncertain Singular Time-delay Systems via Output Feedback Controllers" , 2004, Eur. J. Control.

[15]  M. Mahmoud,et al.  Passivity and passification of time-delay systems , 2004 .

[16]  P. Khargonekar,et al.  Solution to the positive real control problem for linear time-invariant systems , 1994, IEEE Trans. Autom. Control..

[17]  Lihua Xie,et al.  Positive real control problem for uncertain linear time-invariant systems , 1995 .

[18]  Lihua Xie,et al.  Observer-based positive real control of uncertain linear systems , 1999, Autom..

[19]  J. Lam,et al.  Robust D-stability analysis for uncertain discrete singular systems with state delay , 2002 .

[20]  Shengyuan Xu,et al.  Positive real control for uncertain discrete singular systems with state delay , 2002 .

[21]  Henryk Górecki,et al.  Analysis and Synthesis of Time Delay Systems , 1989 .

[22]  Lihua Xie,et al.  Passivity analysis and synthesis for uncertain time-delay systems , 2001 .

[23]  Xi Li,et al.  Criteria for robust stability and stabilization of uncertain linear systems with state delay , 1997, Autom..

[24]  Lihua Xie,et al.  Stability and Positive Realness of Time-Delay Systems , 1999 .

[25]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[26]  A. M. Tsykunov,et al.  Adaptive Control of an Object with a Delayed Control and Scalar Input-Output Signals , 2001 .

[27]  Rogelio Lozano,et al.  On the passivity of linear delay systems , 2001, IEEE Trans. Autom. Control..

[28]  Per Olof Gutman,et al.  Decentralized output-feedback MRAC of linear state delay systems , 2003, IEEE Trans. Autom. Control..

[29]  Chengwu Yang,et al.  H∞ state feedback control for discrete singular systems , 2000, IEEE Trans. Autom. Control..

[30]  Shengyuan Xu,et al.  Robust stability and stabilization for singular systems with state delay and parameter uncertainty , 2002, IEEE Trans. Autom. Control..

[31]  Shengyuan Xu,et al.  Robust stability and stabilization of discrete singular systems: an equivalent characterization , 2004, IEEE Transactions on Automatic Control.