H∞ robust control, linear matrix inequality, state-feedback control
Abstract
Linear matrix inequalities are a powerful tool in the field of robust control for both analysis and synthesis. This work presents a new synthesis formulation for H∞ robust state-feedback control for linear time-invariant systems, continuous time, based on linear matrix inequalities. The formulation include an additional matrix variable, which allows the Lyapunov function to be parameter-dependent, and two adjustment matrices that must be determined a priori. We propose applying a two-step iterative procedure, each step being a problem based on linear matrix inequality, for simultaneously computing the controller gain and the adjustment matrices. The proposed formulation encompasses existing formulations in the literature for specific values of the two adjustment matrices. We present a casestudy to evaluate the proposed formulation.
