Abstract
We consider the problem of synthesizing controllers which minimize a quadratic performance subject to the constraints on H∞ disturbance attenuation as well as on location of the closed-loop poles. This synthesis problem is treated within mixed H2/H∞ design framework by clustering the eigenvalues of the closed-loop system in subregions of the complex plane. To achieve root clustering, a generalized Lyapunov equation is employed. The quadratic (H2) cost is then evaluated in terms of solutions to this generalized Lyapunov and an additional linear matrix equations. H∞-norm constraint is enforced in terms of solution to a Riccati equation which leads to an upperbound on the actual H2 cost. Based on the evaluation of the actual H2 cost, along with the upperbound, an equivalent optimization problem is formulated. Necessary condition for the optimization problem is derived. This condition involves a set of highly coupled equations. Based on descent technique, an iterative algorithm is proposed for solving such coupled equations, and a numerical example is presented.
