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This paper deals with the robust exact pole placement problem in connection with the solvability of a Sylvester equation. The main issue is to compute a wellconditioned solution to this equation. The best candidate solution must possess the minimal condition number. This problem is cast as a global optimization under LMI constraints for which a numerical convergent algorithm is provided and compared with the most attractive methods in the literature.

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This paper presents an application of a piecewise linear control la w in order to obtain the maximal domain of the admissible initial states. This is done in an homothetic w ayto the initial domain generated by the imposed dynamics on the closed-loop of a linear continuous-time system.

This paper deals with sufficient conditions of asymptotic stability and stabilization for nonlinear discrete-time systems represented by a Takagi-Sugeno-type fuzzy model whose state variables take only nonnegative values at all times t for any nonnegative initial state. This class of systems is called positive systems. The conditions of stabilizability are obtained with state feedback control. This work is based on multiple Lyapunov functions. The results are presented in linear matrix inequalities form. A real plant is studied to illustrate this technique.

Laboratoire d'Automatique et d'Etudesdes ProcQd6s Facult6 des Sciences.B.P.Sl5.Marrakech.Morocco. AbstractThis short paper is devoted to the regulator problem for linear discrete-time systems described by the equations : x~+~= Axk + Buk , where U