A new approach for estimating the domain of attraction for linear systems with time-varying delay and saturating actuators

This paper is concerned with the estimation of the domain of attraction for a class of linear continuous-time systems subject to both interval time-varying delay and actuator saturation. A new type of delay-range-dependent condition is firstly proposed using the free-weighting matrix technique to derive a tighter upper bound on the derivative of a Lyapunov-Krasovskii functional. Based on it, a state feedback controller is then designed with the solution of a set of linear matrix inequalities. An optimization problem with LMI constraints is formulated in order to find an initial set as large as possible to obtain a less conservative estimate of the domain of attraction for such systems. An example is carried out to illustrate the theoretical results.