On scalar feedback Nash equilibria in the infinite horizon LQ-game

摘要

In this paper we consider linear stationary feedback Nash equilibria of the scalar linear-quadratic differential game. The planning horizon considered is assumed to be infinite. We present both necessary and sufficient conditions on the system parameters for existence of a unique solution of the associated algebraic Riccati equations (ARE) that stabilizes the closed-loop system. Moreover, we show that in case there exists more than one solution of the (ARE) that stabilizes the closed-loop system, the spectra of the corresponding closed-loop systems almost always differ. A numerical algorithm is given to calculate the solution which yields the most stable closed-loop system.