Static Output Feedback Stackelberg Strategy of Infinite Horizon Markov Jump Linear Stochastic Systems with $H_{\infty}$ Constraint

Abstract

In this paper, a static output feedback (SOF) Stackelberg strategy for continuous-time Markov jump linear stochastic systems (MJLSSs) governed by an Itô differential equation with H _∞ constraints involving multiple decision makers is investigated. First, the linear quadratic regulator (LQR) problem is discussed in terms of the SOF. It is shown that the required solutions can be computed by solving cross-coupled stochastic algebraic Lyapunov type equations (CCSALTEs). Although finding the solutions is based on the classical Lagrange-multipliers technique, the treatment of bilinear matrix inequalities (BMIs) can be avoided. Second, the SOF strategy is also obtained by solving the CCSALTEs for the follower's strategies set. Finally, to demonstrate the existence of the SOF Stackelberg strategy set and the effectiveness of the proposed algorithm, a simple academic example is demonstrated.