Exponential Stability Assignment of Inverse LQ Regulator for Neutral Systems with Time-Varying Delay

Abstract

In this paper, we propose a design method of an inverse LQ regulator for neutral systems with a time-varying delay, in which the resulting system is assured to have a pre-assigned degree of exponential stability. Using this method, the closed-loop system is asymptotically stabilized and a feedback law constructed easily is the optimal control minimizing a class of a cost functional without relation to the exponential stability assignment. In addition, the regulator promises to have a good robust stability as same as ordinary finite dimensional LQ regulators, even when a static nonlinear or a dynamic linear perturbation is inserted in the control input. Finally, the method is demonstrated by numerical examples with and without the exponential stability assignment. In the simulation, it is shown that the proposed method allows designers to seek more fast closed-loop responses by selecting two scalar parameters and the degree of exponential stability in a condition given by LMIs.