Less conservative stability criteria for a class of Lur´e dynamical system with mixed time-varying delays using delay-decomposition approach

This study is focused on the problem of asymptotic stability for a class of Lur´e dynamical system with mixed time-varying delays and nonlinearity. Firstly, by constructing a new appropriate Lyapunov-Krasovkii functional, less conservative delay-dependent stability criteria are derived by using some integral inequalities. Besides, by dividing the mixed delays into many a nonuniformly subintervals and getting the utmost out of some effective mathematical techniques, improved stability criteria are established in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate lesser conservatism and the advantage of the proposed main results.