A game theoretic analysis of a linear compensator in the presence of disturbances and parameter uncertainties

The game-theoretic approach to linear control synthesis, considering both partial and full information, is extended to include system parameter uncertainty. In the present formulation, the initial conditions are constrained to lie within given multidimensional ellipsoids. Global necessary and sufficient conditions are given for the compensator to satisfy the saddle point inequality in differential games. The conditions indicate the exact sets of uncertain parameters and initial conditions for which the saddle inequality will hold. The robustness properties of the compensator are analyzed by extending the results to the infinite-time time-invariant problem