Sufficient conditions for Nash equilibrium point in the linear quadratic game for Markov jump positive systems
Vasile F. Drǎgan, Ivan Ganchev Ivanov · IET Control Theory and Applications · 2017
The infinite horizon linear quadratic differential games for positive linear systems with Markovian jumping is considered. The authors' goal is to propose a set of sufficient conditions that guarantee the existence of the stabilising solution of a system of game theoretic algebraic Riccati type equations associated to the considered differential game. To this end the authors' introduce a new type of solution of the Riccati equation namely the strong stabilising solution and they prove that this strong stabilising solution is just a stabilising solution of this kind of Riccati equation. The main contribution is the formulation of a set of sufficient conditions which guarantee the convergence of the proposed iterative procedure to the stabilising solution of game theoretic algebraic Riccati type equation. Finally, a numerical example shows the performance of the proposed algorithm.