Quadratic $\mathcal{L}_{2}$ Performance Analysis of Switched Uncertain Linear Systems

We analyze quadratic
$\mathcal{L}_{2}$
performance (quadratic stability and certain
$\mathcal{L}_{2}$
gain) for switched uncertain linear systems (SULS) with norm-bounded uncertainties. Assuming that no single subsystem achieves quadratic
$\mathcal{L}_{2}$
performance
$\gamma$
but a convex combination of the subsystems can make it, we propose a state-dependent switching law such that the SULS achieves the same performance.