Full State Feedback Control Design for “Delay Scheduling”

A fixed full state feedback controller design approach is proposed for linear time invariant (LTI) systems with time delays. This approach enables the designer to use recently introduced “delay scheduling” procedure, which opens a new direction in control synthesis. “Delay scheduling” strategy suggests prolonging the existing (and unavoidable) delays in order to recover stability or to improve the control performance features. To be able to do this, however, system should have multiple stable operating zones in the domain of the delays. The main contribution of this paper is to develop a procedure for designing such a control law. It starts with a simple usage of LQR for non-delayed systems. This approach, nevertheless, imparts some complexities when delays are introduced. We handle them using a recent paradigm, called the Cluster Treatment of Characteristic Roots (CTCR). For an example to the ensuing design strategy, we use a fully actuated cart-pendulum system. Relevant simulations are carried out to show the viability of the proposed idea.