Some Results on Guaranteeing Cost Strategies: Full-block Multipliers and Fictitious Games

Guaranteeing cost robust minimax controls are determined for a discrete-time linear system with uncertainty of linear fractional form over infinite horizon by means of the full-block multiplier technique. It is highlighted in what sense this technique can be considered as the extension of other approaches applying a single adjustable parameter in the derivation of the linear matrix inequalities to be solved. Moreover, it is shown how to construct a fictitious game with completely known dynamics and with a cost criterion parametrized by the full-block multipliers in such a way that the minimax strategy and the upper value for it turn out to be the robust minimax strategy and the guaranteed cost for the original uncertain system.