Stabilization of Nonlinear Continuous–Discrete Dynamic Systems with a Constant Sampling Step

This paper considers nonlinear continuous–discrete (hybrid) systems containing two subsystems of differential and difference equations, respectively, and one-dimensional (scalar) or multidimensional (vector) control. The transition from a nonlinear hybrid system with a constant sampling step h > 0 to an equivalent, in a natural sense, nonlinear discrete dynamic system is presented. Sufficient conditions are established, first, for reducing the first approximation systems of nonlinear discrete systems to the Brunovsk´y canonical form and, second, for stabilizing such systems and nonlinear hybrid systems with control of different dimensions. Algorithms for constructing stabilizing control laws for nonlinear hybrid systems are developed. Numerical examples are provided to illustrate the effectiveness of this approach to stabilizing nonlinear hybrid dynamic systems.