Robust stabilization of uncertain multi-state-delay systems

A new delay-independent stability criterion and some stabilizable conditions are presented in the form of an algebraic Riccati equation for the certain delay systems with time-varying multi-state-delay. Then some sufficient conditions for the robust stabilizability are derived for this class of uncertain systems. Furthermore, if there exists a positive-definite symmetric solution satisfying the algebraic Riccati equation or the algebraic Riccati inequality, a suitable memoryless linear feedback law can be derived. In this paper, the uncertainties do not need to satisfy the matching condition and the rank-one decomposition does not need to be done