Canonical Forms and Switching Laws for Linear Switched Systems

The class of continuous-time time-invariant controllable linear systems can be stabilized by the use of controller canonical forms. Such canonical forms are not known in the context of switched control systems since a simultaneous transformation of two or more linear systems is not trivial and straightforward. Here, the attention is focused in developing such canonical forms for controllable switched systems consisting of two continuous-time time-invariant linear subsystems by constructing the simultaneous transformation matrices by arranging the suitably chosen basis vectors of the state space of the system of our interest as columns. These canonical forms are then used to devise switching strategies to control any arbitrary initial state to the origin by switching among the subsystems of the switched system of our interest.