Stabilization of 2D continuous systems with multi-delays and saturated control

This paper deals with the problem of stabilizability with saturated control of 2D continuous systems with multi-delays. State feedback control is used. Sufficient conditions for asymptotic stability are presented. The synthesis of the required controllers is given under LMI form. An illustrative example is treated.

[1]  A. Benzaouia,et al.  The resolution of equation XA+XBX=HX and the pole assignment problem , 1994, IEEE Trans. Autom. Control..

[2]  Tingshu Hu,et al.  Analysis and design for discrete-time linear systems subject to actuator saturation , 2002, Syst. Control. Lett..

[3]  Tadeusz Kaczorek,et al.  LMI approach to stability of 2D positive systems , 2009, Multidimens. Syst. Signal Process..

[4]  Tingshu Hu,et al.  The equivalence of several set invariance conditions under saturation , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[5]  C. Burgat,et al.  Regulator problem for linear discrete-time systems with non-symmetrical constrained control , 1988 .

[6]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

[7]  W. Marszalek Two-dimensional state-space discrete models for hyperbolic partial differential equations , 1984 .

[8]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[9]  Abdellah Benzaouia,et al.  The Regulator Problem for Linear Systems With Saturations on the Control and its Increments or Rate: An LMI Approach , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  A. Saberi,et al.  Semi-global stabilization of linear discrete-time systems subject to input saturation via linear feedback-an ARE-based approach , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

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

[12]  Ali Saberi,et al.  Semiglobal stabilization of linear discrete-time systems subject to input saturation, via linear feedback-an ARE-based approach , 1996, IEEE Trans. Autom. Control..

[13]  T. Kaczorek REALIZATION PROBLEM FOR POSITIVE 2-D ROESSER TYPE MODEL , 1997 .

[14]  Abdellah Benzaouia,et al.  Stabilization of 2D saturated systems by state feedback control , 2010, Multidimens. Syst. Signal Process..

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

[16]  R. Roesser A discrete state-space model for linear image processing , 1975 .

[17]  Ettore Fornasini,et al.  Doubly-indexed dynamical systems: State-space models and structural properties , 1978, Mathematical systems theory.

[18]  Donald D. Givone,et al.  Multidimensional Linear Iterative Circuits - General Properties , 1972, IEEE Trans. Computers.

[19]  S. Niculescu Delay Effects on Stability: A Robust Control Approach , 2001 .

[20]  Abdellah Benzaouia,et al.  Regulator problem for linear systems with constraints on control and its increment or rate , 2004, Autom..

[21]  Shengyuan Xu,et al.  Robust stability and stabilisation of 2D discrete state-delayed systems , 2004, Syst. Control. Lett..

[22]  Abdellah Benzaouia,et al.  On Improving the Convergence Rate of Linear Continuous-Time Systems Under Constrained Control With State Observers , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[23]  A. Hmamed Constrained regulation of linear discrete-time systems with time delay: Delay-dependent and delay-independent conditions , 2000, Int. J. Syst. Sci..

[24]  Abdellah Benzaouia,et al.  Piecewise linear constrained control for continuous-time systems , 1999, IEEE Trans. Autom. Control..

[25]  Abdellah Benzaouia,et al.  Stabilization of linear systems with saturation: a Sylvester equation approach , 2004, IMA J. Math. Control. Inf..

[26]  A. Hmamed,et al.  Regulator problem for linear continuous-time delay systems with nonsymmetrical constrained control , 1995, IEEE Trans. Autom. Control..

[27]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..