Sirenko A. Investigation of the stability of dynamic systems with switching and delay

This dissertation is devoted to important problems of applied mathematics, namely – development methods of study the dynamics of processes wich modeled by a set of differential and difference equations for switching. The main attention is concentrated on one of the main tasks of analysis of the dynamics such systems, namely the study of sustainability as a key quality properties which essential for the design of control systems. At the work was constructive receipt assess the stability of linear and weakly nonlinear systems, in particular with delay, consisting of subsystems described by linear differential and difference equation. Also were delivered and solved the following key objectives: – obtain sufficient conditions for the existence of a common Lyapunov function for switching systems; – substantiated acceptable estimates disturbances difference systems with late, in which the asymptotic stability of systems was kept; – using the method functions Lyapunov received asymptotic stability conditions weakly nonlinear systems; In dissertation I received the following new results: for the first time: - was obtain the conditions for the existence of a common Lyapunov function for systems of linear differential and difference systems; - was obtain the conditions of asymptotic stability of the zero equilibrium state systems with switching; - was obtain design conditions for the asymptotic stability of stationary systems with a delay; improved: - the conditions of interval stability and the valuation of convergence of the difference systems; got further development: - conditions of stability of systems with delay. The obtained results can be used in tasks study the stability of dynamics flying apparatus, intelligent transportation systems, systems of automatic temperature control, and other mathematical models, which are characteristic of hybrid systems.