Stabilization of Continuous‐Time Delay Systems by a Partially Delay‐Dependent Controller: A Stochastic Method

ABSTRACT This paper proposes a novel partially delay‐dependent controller for continuous‐time delay systems via a stochastic method. In order to make full use of the probability distributions of delay and non‐delay terms, new delay‐dependent stabilization results are obtained based on the Markov process rather than the Bernoulli variable. Particularly, the transition rate matrix (TRM) of Markov process is designed to reduce conservativeness and achieve a larger delay bound via solving an optimization problem. To reduce the computational complexity coming from the included equality constraints, another method based on the TRM given beforehand is given by using strict LMIs, which is also less conservative than traditional methods. Moreover, some special situations can be obtained directly and illustrate the wider universality of the proposed methods. Finally, an example is used to demonstrate the utility and advantage of the methods.