Stability of Linear Systems with Time Delay: A New Delay Fractioning Based Lyapunov-Krasovskii Approach

This paper investigates the stability of linear systems with time delay. Both single delay and multiple delay cases are considered respectively. The criteria of stability is derived based on a new type of Lyapunov-Krasovskii functional and is formulated as feasibility problems of Linear Matrix Inequalities. Less conservative stability conditions are obtained through a new delay fractioning approach, and the conservatism can be reduced as the delay fractioning grows. When time-varying norm-bounded uncertainties appear in the delay system, the robust delay-dependent stability condition is also given. Numerical examples are provided to illustrate the effectiveness of our main results.