Disturbance attenuation analysis of state feedback Nash strategy for Linear Quadratic Sequential Games

There is limited formal mathematical analysis of one type of games - dynamic sequential games with large, or even infinitely large, planning horizons, from the point view of system controls. In this paper, we use a zero-sum game theoretical approach to address the disturbance attenuation analysis of state feedback Nash strategies for Dynamic Linear Quadratic Sequential Games (LQSGs) with uncertainties or disturbances. For finite-horizon LQSGs, we first provide state feedback Nash strategies with optimal attenuation levels. Then we extend the approach to infinite-horizon LQSGs. We prove that the feedback system is Bounded Input Bounded Output (BIBO) stable with respect to the disturbances.