Improved Stability Criteria for Time-Varying Delay System Using Second and First Order Polynomials

This article concerns the problem of stability analysis of systems with time-varying delay. Recent developments in this direction involves approximation of a second order polynomial function of time-delay. This article proposes a new Lyapunov-Krasovskii Functional that does not introduce the second-order polynomial and thereby avoid the approximation involved in obtaining the stability criterion. Two stability criterion are presented, one introduces the second-order polynomial and the other one does not. A comparison using numerical examples shows that the avoidance of second-order polynomial formulation leads to improved results.