Lukashiv T. Stability and stabilization of stochastic dynamic systems of random structure with external Markov switchings

The actual problems of stability and stabilization of stochastic dynamic systems of random structure with external Markov switchings are investigated in this thesis. The sufficient conditions of asymptotical global stability, asymtotical mean square stability of solution of stochastic dynamic systems of random structure with external Markov switchings are obtained. The necessary and sufficient conditions of exponential mean square stability of solution of linear stochastic dynamic systems of random structure are obtained. The optimal stabilization problem for strong solution of diffusion dynamic system of random structure with external Markov switchings is solved.