Improved stability criterion and output feedback control for discrete time-delay systems

This paper investigates the stability and stabilization for a class of linear systems with time-varying delay. We provide a new finite-sum inequality which is a powerful tool for stability analysis of time-delay systems. Applying the inequality, a new stability criterion is proposed in terms of linear matrix inequalities (LMIs). We also design a method for static output feedback (SOF) control problems which contains two parts. The first part is to find an initial values of the matrix variables. By utilizing the initial values, the condition for SOF control problems can be solved by an improved path-following method. Numerical examples demonstrate the effectiveness of the stability criterion and the SOF stabilization method.