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# Nash games and mixed *H*_{2}/*H*_{∞} control

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## Abstract

The established theory of non-zero sum games is used to solve a mixed *H* _{2}/*H* _{∞} control problem. Our idea is to use the two pay-off functions associated with a two player Nash game to represent the *H* _{2} and *H* _{∞} criteria separately. We treat the state feedback problem, and we find necessary and sufficient conditions for the existence of a solution. A full stability analysis is available in the infinite horizon case [13], and the resulting controller is a constant state feedback law which is characterised by the solution to a pair of cross-coupled Riccati differential equations.

## Keywords

Nash Equilibrium Riccati Equation Nash Equilibrium Strategy Nash Solution Nash Game
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© Springer-Verlag 1992