Abstract

In this thesis, the problem of state observation for a class of impulsive switched systems is addressed. Corresponding to each subsystem, an identity Luenberger observer is employed and a switching observer is constructed accordingly. The asymptotic stability property of the proposed switching observer is discussed and LMI-based algorithms are given which provide necessary conditions for the asymptotic stability of the switching observer for the switching signals with an average dwell time greater than a specific value. Since switched systems without impulse are a special case of impulsive switched systems, all the results in this work can be applied to design observers for switched systems without impulse. The design of finite time switching observers for a class of linear switched systems is another problem addressed in this work. The finite convergence time property of the proposed switching observer is discussed and the exponential stability of the observation error is investigated. An LMI-based algorithm is given which provides conditions for the exponential stability of the switching observer. Finally, the idea of finite time observers for linear continuous time systems is extended to linear time invariant discrete time systems. The main motivation for this extension is that unlike the famous dead-beat observers designed for discrete time systems, the proposed observer in this work need not place all the eigen-values at the origin, which leads to a much more flexible design compared to the existing techniques.