ANALYSIS OF PRACTICAL STABILITY AND LYAPUNOV STABILITY OF LINEAR TIME-VARYING NEUTRAL DELAY SYSTEMS

Practical stability guarantees trajectories of a dynamical system bein g bounded within a prespecified region during a specified time interva l and is of great interest in many applications. For a class of linear time-varying systems described by delay differential equations of neu tral type, concepts of practical stability involving both variations o f the state and its derivative are introduced in terms of given estima te 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 r esults are then applied to the Lyapunov stability and positively invar iant tubes of the corresponding homogeneous systems. Specifically, an algebraic condition of globally exponentially asymptotical stability i s derived, which is related to the well known property of the M-matrix and is independent of delay. Finally, an illustrative example is give n.