A novel approach to exponential stability of continuous-time Roesser systems with directional time-varying delays

This paper addresses the problem of exponential stability analysis of two-dimensional (2D) linear continuous-time systems with directional time-varying delays. An abstract Lyapunov-like theorem which ensures that a 2D linear system with delays is exponentially stable for a prescribed decay rate is exploited for the first time. In light of the abstract theorem, and by utilizing new 2D weighted integral inequalities proposed in this paper, new delay-dependent exponential stability conditions are derived in terms of tractable matrix inequalities which can be solved by various computational tools to obtain maximum allowable bound of delays and exponential decay rate. Two numerical examples are given to illustrate the effectiveness of the obtained results.