The Stability of Continuous-Discrete Dynamical Systems under Fast Switching

The paper considers the problem of the influence of switching moments on the stability of the equilibrium points of nonlinear continuous-discrete dynamical systems. New stability criteria based on the methods of the perturbation theory of linear operators are proposed. The main attention is paid to obtaining stability signs of the equilibriumpoints of continuous-discrete systems under fast switching of the system dynamics. The applications to the stability problem of the equilibriumpoints of the systems with one-dimensional and two-dimensional phase spaces of a continuous system are considered. The results obtained are formulated in the terms of the initial equations and brought to the calculation formulae and algorithms. The effectiveness of the proposed formulae is illustrated by considering a model example.