Multiobjective robust control of LTI systems subject to unstructured perturbations

We consider a multiobjective robust controller synthesis problem for an LTI system subject to unstructured perturbations. Our design specifications include robust stability, robust performance (H₂-norm) bounds and time-domain bounds (output and command input peak). We derive sufficient conditions, based on a single quadratic Lyapunov function, for the existence of an LTI controller such that the closed-loop system satisfies all specifications simultaneously. These conditions can be numerically checked using finite-dimensional, convex optimization over LMIs, associated with a two-dimensional search. When considering only a subset of the specifications, we recover previous results from the literature, such as those obtained in mixed H₂/H_∞ control.