Title: Stability of linear switching system with delayed feedback control (½ hour)
Abstract: We consider a switching system consisting of a finite number of linear systems with delayed feedback. It has been shown that the stability of a switching system composed of linear ODE systems may be achieved by using a ``Single Lyapunov Function Method'' switching rule. Here we extend this result to a class of delayed systems.
In our model there are N subsystems, each having an unstable ODE part and a delayed feedback control. We modify the switching rule for ODE systems to a ``Single Lyapunov Functional Method'' switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati type Lyapunov functional under a condition on the time delay.