Analysis of stability problem of dynamical systems by optimization methods

In this thesis some stability problems of linear systems are investigated. Both continuous systems (Hurwitz stability) and discrete systems (Schur stability) are considered. For interval plane systems necessary and sufficient conditions for the existence of common Lyapunov functions are obtained and illustrative example are given. Similar problem is investigated for 3 × 3 interval systems, the existence conditions are obtained. The obtained results are transformed into appropriate algorithms. These algorithms are simple and faster. Given n × n dimensional interval systems of Z-matrices a necessary and sufficient condition is proved. For an arbitrary interval system one sufficient condition for the existence of a common diagonal solution to Lyapunov matrix inequality is obtained. One algorithm for first order stabilizator for interval plants is proposed. Sufficient condition for the stability margin of discrete systems is obtained. The obtained results are illustrated by number of examples.