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New results for delay-dependent stability of linear systems with time-varying delay

The asymptotic stability problem for a class of linear systems with time-varying delays is studied using a generalized discretized Lyapunov functional approach. The kernel of the functional, which is a function of two variables, is chosen as piecewise linear. The conditions of the Lyapunov functional and its derivative are written in terms of linear matrix inequalities (LMIs). New delay-dependent stability criteria are proposed by simplifying the derived LMIs. Numerical examples show that the results obtained by these new criteria significantly improve the estimate of stability limit over the existing results in the literature.