
In this chapter, two directions are explored: the first concerns the synthesis of non saturating controllers, while the second direction deals with controllers tolerating saturations to take effect. The second method was firstly used in [22] with the use of a multiple Lyapunov function. However, only the intersection of all the corresponding level sets of the local functions was considered as a region of asymptotic stability of the switching system. This drawback is improved in [25, 35] by considering, for the first time, a large set of asymptotic stability composed by the union of all the level sets. In this context, different sufficient conditions of asymptotic stability are obtained for switching systems subject to actuator saturations. Furthermore, these conditions are presented in the form of LMIs for the state feedback control case.
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