Stability of discrete state delay systems

A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N-th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed. The proposed stability condition ensures stability of a discrete state delay system whose state delay is not exactly known but only known to lie in a certain interval.