Stability and stabilization of discrete-time systems with time-delay via Lyapunov-Krasovskii functional

The stability and stabilization problems for discrete systems with time-delay are discussed .The stability and\ud stabilization criterion are expressed in the form of linear matrix inequalities (LMI). An effective method\ud allowing us transforming a bilinear matrix Inequality (BMI) to a linear matrix Inequality (LMI) is developed.\ud Based on these conditions, a state feedback controller with gain is designed. An illustrative numerical example\ud is provided to show the effectiveness of the proposed method and the reliability of the results