Robust gain-scheduled control of a class of nonlinear parameter-dependent systems: application to an uncertain inverted pendulum

Given a nonlinear parameter-dependent system, we seek an output feedback controller such that the closed-loop system satisfies a number of specifications. Our specifications include stability, command input and output peak bounds. The controller state-space matrices are allowed to depend on a set of measured parameters and/or nonlinearities, if any. Our specifications must be satisfied robustly with respect to the remaining (unmeasured) parameters and/or nonlinearities. We derive sufficient conditions that ensure the existence of such a "mixed" gain-scheduled/robust controller. These conditions are LMIs, associated with a set of nonconvex conditions. We propose an efficient heuristic to solve them, and illustrate our design method with an inverted pendulum example.