Hierarchical stability conditions for aperiodic sampled-data control systems with fixed delay

This paper deals with the stability issue of aperiodic sampled-data control systems with fixed delay. First, to obtain the less conservative stability criterion, the hierarchical looped-functional is assembled. In the functional, the integrals in the integral inequalities are directly utilized in the construction. Hence, the integrals of the system equation are prevented to avoid the products of the free matrices and system matrices. Also, the integrals over the segmented interval $[t,t-\gamma ]$ are introduced. Then, by employing the generalized free-matrix-based integral inequalities, the integrals of the same quadratic product term over different time intervals are estimated to acquire the linear functions of these intervals. Next, the hierarchical stability conditions are presented in terms of the linear matrix inequalities based on the Schur complement. Finally, some numeric examples are used to illustrate the superiority of the proposed method.