A unified convex combination approach to switched uncertain nonlinear systems

We address a unified convex combination approach to a class of switched uncertain nonlinear systems, focusing on quadratic stability and ℒ2 gain. In each subsystem, there are norm-bounded uncertainties in the system matrix and nonlinear terms with quadratic constraints. The proposed convex combination is original and unified in the sense of incorporating not only the nominal subsystem matrices but also uncertainty and quadratic constraints in the same form. When there is no single subsystem having the desired performance but a convex combination of subsystems does, we design a switching law so that the switched system achieves the same performance. Moreover, the discussion is extended to switching state feedback and its application to a boost converter.