Robust Stability and Synthesis of Discrete Systems for Nonlinear Objects Control

摘要

On the basis of the Lyapunov functions in the form of norm of the vector of state we obtained sufficient conditions of the robust stability in the domain of nonlinear non-stationary discrete systems (which can be verified constructively), for which parameters their guaranteed multiple estimates are set. These sufficient conditions can be verified in constructional way. For strictly monotonous nonlinear functions verification of these sufficient conditions is reduced to necessity of solving the combinatorial problems in the space of states. On the basis of the obtained sufficient conditions of robust stability we solved the problems of synthesis for systems of stabilization of nonlinear control objects. Since the stabilizing in the domain controls were obtained from solving minimax problems, then they cannot guarantee stability of closed systems in the domain for arbitrary multiple estimates of object control parameters. Therefore, verification of fulfilment of sufficient conditions of robust stability in a domain for given multiple estimates of parameters and in the domain X is the final stage of problem solving for synthesis of control.