Positive effects of time delays on the stability of switched control systems with partial state feedback information

Abstract

In this paper, a novel state-dependent switching controller with delayed positive partial state feedback is proposed to stabilise a controlled system with insufficient state information. At first, the controlled system is converted to a single-degree-of-freedom vibrational system by using an invertible transform and a second-order Taylor approximation for the time delay term. Then, appropriate control gain parameters and a state-dependent switching rule are designed via the physical meaning of the resulting vibrational system. By combining the advantages of delayed positive position feedback with the state-dependent switching mechanism, we find that the time delay can considerably improve the asymptotic stability of the controlled system. Finally, three numerical examples show that the proposed controller is effective and that time delay indeed plays a prominent positive role in switched control systems.