Switching observers for continuous-time and discrete-time linear systems

An approach to estimation for continuous-time and discrete-time linear systems is proposed that is based on the idea of using switching observers. Convergence conditions have been found to ensure the stability of the error dynamics; in addition, they guarantee the existence of an upper bound to a quadratic cost function of the estimation error. The observer gains may be selected by solving a set of linear matrix inequalities (LMIs). A method is described to design a switching observer that aims to minimize the upper bound to the estimation cost function. Moreover, such a design may be efficiently accomplished by using an LMI algorithm.