Robustness analysis of global exponential stability of nonlinear systems with generalized piecewise constant arguments

On account of the finite propagation speed of signals, time-delay phenomena are abundant. Compared with time-delay systems, nonlinear systems with generalized piecewise constant arguments can be both of advance and retard, which are an extension to time-delay systems. In this paper, we address the robustness of global exponential stability for a general class of nonlinear systems with generalized piecewise constant arguments, that is, given globally exponentially stable nonlinear systems, the problem that how much intensity of generalized piecewise constant arguments the nonlinear systems can be sustained to maintain globally exponentially stable is investigated. First, conditions guaranteeing the existence and uniqueness of solution for a general class of nonlinear systems with generalized piecewise constant arguments are formulated. Furthermore, the upper bound of the intensity of generalized piecewise constant arguments can be obtained to keep the nonlinear systems to be globally exponentially stable by solving the transcendental equation. Finally, one numerical example is presented to show the effectiveness of theoretical result.