Quadratic Stabilization and ℒ2 Performance Design of Switched Uncertain Affine Systems

We deal with quadratic stabilization (QS) and ℒ
2
performance design for switched systems which are composed of a finite set of uncertain affine subsystems. In each subsystem, there exists norm bounded uncertainty in the system matrix, and the vector field includes a nonlinear term with quadratic constraint. Under the assumption that there is a convex combination of subsystems’ affine vectors reaching the origin, we construct a convex combination of subsystems (CCS) without an affine vector, by using the coefficients in the convex combination of affine vectors. If the CCS is QS at the origin, then we design a state-dependent switching law under which the switched uncertain affine system (SUAS) is also QS at the origin.