Quadratic Stabilization and L_2 Gain Analysis of Switched Affine Systems

摘要

We consider quadratic stabilization and L_2 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 L_2 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 L_2 gain analysis under state feedback.