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We investigate the stabilizability of discrete-time linear switched systems,when the sole control action of the controller is the switching signal, andwhen the controller has access to the state of the system in real time. Despitetheir apparent simplicity, determining if such systems are stabilizable appearsto be a very challenging problem, and basic examples have been known for long,for which the stabilizability question is open. We provide new results allowingus to bound the so-called stabilizability radius, which characterizes thestabilizability property of discrete-time linear switched systems. Theseresults allow us to compute significantly improved explicit lower bounds on thestabilizability radius for the above-mentioned examples. As a by-product, weexhibit a discontinuity property for this problem, which brings theoreticalunderstanding of its complexity.

Lower bounds and dense discontinuity phenomena for the stabilizability radius of linear switched systems