Nash Equilibrium for 2nd-order Two-Player Non-Zero Sum LQ Games with Executable Decentralized Control Strategies

Riccati equations are the basis to construct Nash equilibrium solutions for linear quadratic (LQ) non-cooperative games when players apply linear state feedback strategies. Diagonal-form solutions of the Riccati equation associated with a second-order two-player non-zero sum linear quadratic game is discussed and the Nash equilibrium can be implemented by decentralized control strategies. The result is also extended to a high order two-player linear quadratic game