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Quadratic stabilization and L2 gain analysis of switched affine systems

We consider quadratic stabilization and L2 gain analysis for switched systems which are composed of a finite set of time-invariant affine subsystems. Both subsystem matrices and vectors are switched, and no single subsystem has desired quadratic stability or specific L2 gain property. We show that if a convex combination of subsystem matrices is Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched system is quadratically stable. The result is also extended to L2 gain analysis under state feedback.