Robust stabilization of uncertain systems with time-varying multistate delay

In this paper, the authors deal with the problem of stabilizing a class of uncertain linear systems with time-varying multi-state delay and subject to norm-bounded parameter uncertainty via memoryless linear state feedback. Some sufficient conditions for the robust stabilizability are derived for this class of uncertain systems. If there exists a positive-definite symmetric solution satisfying the algebraic Riccati equation (or inequality), a suitable memoryless state feedback law can be derived also. Moreover, all such parametric algebraic Riccati inequalities have been transformed into some linear matrix inequality problems, so there is no tuning of the parameters to gain a stabilizing solution.