A convex optimization approach to fixed-order controller design for disturbance rejection in SISO systems

The problem of rejection of persistent unknown-butbounded disturbances can be solved using the wellknown I1 design approach. However, in spite of its success, this theory suffers from the fact that the resulting controller may have arbitrarily high order, even in the state-feedback case. In addition, system performance is optimized under the assumption of zero initial conditions. In this paper we propose a new approach to the problem of synthesizing k e d order controllers to optimally reject persistent disturbances. The main result of the paper shows that this approach leads to a finite-dimensional convex optimization problem that can be efficiently solved.