I. introduction
This paper studies the stability of linear systems with input asymmetric constraints on thecontrol. A main problem which is always inherent to all dynamical systems is the presence of actuators saturations. The class of systems with saturations has obtained great interest duringthe two last decades. Even for linear systems, this problem has been an active area of research for many years. Two main approaches have been developed in the literature.:
The first is the so-called positive invariance approach, which is based on the design of controllers which work inside a region of linear behavior where saturations do not occur (see [2], [11], [10], [11] and the references therein). The stabilizing gain regulator obtained with this approach is a solution to the non linear algebraic equation , where matrix satisfies the main condition of positive invariance. One can quote the work of [4] and [6] where the resolution of equation is presented as a technique of partial eigenstructure assignment. This resolution was also associated to the constrained regulator problem.