Robust Positive Real Synthesis for 2D Continuous Systems via State and Output Feedback

AbstractThis paper considers the problem of positive real control for uncertain twodimensional (2D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm bounded in both state and measurement output equations. The purpose is the design of controllers such that the resulting closed-loop system is asymptotically stable and strictly positive real for all admissible uncertainties. A version of the positive realness of 2D continuous systems is established. Then, sufficient conditions for the solvability of the positive real control problem via state feedback and dynamic output feedback controllers, respectively, are proposed. A linear matrix inequality approach is developed to construct the desired controllers. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the proposed method.

[1]  Shengyuan Xu,et al.  An LMI approach to guaranteed cost control for uncertain linear neutral delay systems , 2003 .

[2]  Ian R. Petersen,et al.  An LMI approach to output-feedback-guaranteed cost control for uncertain time-delay systems , 2000 .

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

[4]  Shengyuan Xu,et al.  Robust H∞ Output Feedback Control for Uncertain Distributed Delay Systems , 2003, Eur. J. Control.

[5]  Lihua Xie,et al.  H[∞] control and filtering of two-dimensional systems , 2002 .

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

[7]  E. Rogers,et al.  Positive real control of two-dimensional systems: Roesser models and linear repetitive processes , 2003 .

[8]  M.N.S. Swamy,et al.  A new method for computing the stability margin of two-dimensional continuous systems , 2002 .

[9]  Jong Hae Kim,et al.  H∞-output feedback controller design for linear systems with time-varying delayed state , 1998, IEEE Trans. Autom. Control..

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

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

[12]  D. Bernstein,et al.  Explicit construction of quadratic lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. part II: Discrete-time theory , 1993 .

[13]  Nikos E. Mastorakis,et al.  Stability margin of two-dimensional continuous systems , 2000, IEEE Trans. Signal Process..

[14]  Panajotis Agathoklis,et al.  The discrete-time strictly bounded-real lemma and the computation of positive definite solutions to the 2-D Lyapunov equation , 1989 .

[15]  J. Lodge,et al.  The bilinear transformation of two-dimensional state-space systems , 1982 .

[16]  K. Galkowski,et al.  Positive real control for uncertain two-dimensional systems , 2002 .

[17]  Brian D. O. Anderson,et al.  Stability and the matrix Lyapunov equation for discrete 2-dimensional systems , 1986 .

[18]  T. Kaczorek.  Two-Dimensional Linear Systems , 1985 .

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

[20]  Krzysztof Galkowski,et al.  LMI based stability analysis for 2D continuous systems , 2002, 9th International Conference on Electronics, Circuits and Systems.

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