Quadratic Stabilization and $\mathcal{L}_{2}$ Performance Design of Switched Uncertain Nonlinear Systems

Quadratic stability (QS) and
$\mathcal{L}_{2}$
performance are studied for switched systems consisting of nonlinear subsystems with norm-bounded uncertainties and quadratic constraints for nonlinearities. When no single subsystem is QS, if there exists a convex combination of subsystems which is QS, then a state-dependent switching law, based on the convex combination of subsystems, is proposed under which the entire switched system is QS. Then, the discussion is extended to the case concerning quadratic
$\mathcal{L}_{2}$
performance, and parallel results are obtained.