Third order switched linear systems

Resum

In this thesis different types of properties of switched systems are studied. Reachability problem of switched systems is handled first, where the reachable set from an initial condition of a second order switched nonlinear system is described. States of the reachable set is not only calculated but the appropriate switching law is explicitly given. A method for stabilization a switched linear system is described. The method is performed by split the variable by using a projection on a linear subspace. The conditions of the result are restrictive since the result asks that the subsystems share an invariant linear subspace. A particular condition for stabilization of third order switched system is given when subsystems have a common eigenvector, in this case the stability property of the third order switched system is simplified to the stability property of a second order switched system. The problem of stabilization for third order switched systems is dealt. First we study a class of switched linear systems of third order where a switching law is found such that the system has an invariant set. This invariant set is a cone generate by three vectors, then by a linear change of variables we can set the invariant set as the positive octant. We have provided conditions for stabilization of the class of third order switched systems. The problem of stabilization also is studied for switched linear systems of higher order which is based on minimization the distance of the trajectory to the origin. Necessary and sufficient conditions are given for stabilization switched systems. It is shown that this method agrees with the known method for second order switched linear systems.