Robust Simultaneous Stabilization Via Minimax Adaptive Control

The paper explores the usage of minimax adaptive controllers to guarantee finite
$\mathcal{L}_{2}$
-gain simultaneous stabilization of linear time-invariant (LTI) plants. It is shown that a minimax adaptive controller simultaneously stabilizes any two multiple-input multiple-output (MIMO) P-stabilizable LTI plants when no LTI controller can achieve that, and the worst attained
$\mathcal{L}_{2}$
-gain bound for the transient dynamics is readily computable.