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

The problem of rejection of persistent unknown-but-bounded disturbances can be solved using the well-known l¹ 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 fixed 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