Two-dimensional state-space digital filters with minimum frequency-weighted l2-sensitivity under l2-scaling constraints

The minimization problem of frequency-weighted l
2
-sensitivity subject to l
2
-scaling constraints is formulated for two-dimensional (2-D) state-space digital filters described by the Roesser model. It is shown that the Fornasini-Marchesini second model can be readily imbedded in the Roesser model. An iterative method is developed to solve the constrained optimization problem. This method converts the problem into an unconstrained optimization formulation by using linear-algebraic techniques and solves it by applying an efficient quasi-Newton algorithm. A case study is presented to illustrate the utility of the proposed technique.