Analysis of practical stability and Lyapunov stability of linear time-varying neutral delay systems

Abstract

Practical stability guarantees trajectories of a dynamical system being bounded within a prespecified region during a specified time interval and is of great interest in many applications. For a class of linear time-varying systems described by delay differential equations of neutral type, concepts of practical stability involving both variations of the state and its derivative are introduced in terms of given estimate sets. Sufficient conditions of practical stability are established on the basis of the mixed differential difference comparison principle presented in this paper, in terms of coefficients of the systems and the given allowable trajectory bounds. For the case of time-invariant estimate sets, these conditions are also independent of delay. These results are then applied to the Lyapunov stability and positively invariant tubes of the corresponding homogeneous systems. Specifically, an algebraic condition of globally exponentially asymptotical stability is derived, which is related to the well known property of the M-matrix and is independent of delay. Finally, an illustrative example is given.