Robust optimal pole-placement in a vertical strip and disturbance rejection

Abstract

This paper presents a linear quadratic regulator (LQR) for robust closed-loop pole-placement within a vertical strip, and disturbance rejection with an H _∞-norm constraint for the uncertain linear systems. The concerned systems cover both matched and mismatched uncertain linear systems with unstructured or structured uncertainties existing in both the system and input matrices. A set of tuning parameters is incorporated for some flexibility in finding a solution to the algebraic Riccati equation, and a controller gain parameter is selected for robust pole clustering. Also, a constraint is established to verify whether the proposed robust LQRs preserve H ₂ optimality with respect to a specific quadratic cost function.