Based on state space reachable sets we formulate a two-player differential game for stability. The role of one player (the bounded disturbance) is to remove as much of the system's stability as possible, while the second player (the control) tries to maintain as much of the system's stability as possible. To obtain explicit computable relationships we limit the control selection to setting basic parameters of the system in their stability range and the disturbance is a bounded scalar function. This stability game provides for an explicit quantification of uncertainty in control systems and the value in the game manifests itself as the L=-gain of the dynamic input/output disturbance system as a function of the control parameters. It has been discovered recently that the L=-gain can be expressed as an explicit parametric formula for linear second order games, and design charts here provide quantitative information in third order linear games. A model predictive scheme will be given for the higher order linear and nonlinear stability games.
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