Novel Exponential Estimate for Nonlinear Systems with Mixed Interval Time-Varying Nondifferentiable Delays

Abstract

This paper addresses exponential stability problem for a class of nonlinear systems with mixed time-varying delays. The time delays are non-differentiable functions belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov’s functional, new criteria for the exponential stability of the system are established in terms of linear matrix inequalities. The result has been applied to robust stability problem of uncertain systems with interval time-varying delays. Numerical examples are given to show the effectiveness of the conditions.