Synthesis of robust strictly positive real discrete-time systems with l2 parametric perturbations

The author addresses the robust strict-positive realness problem for families of discrete-time polynomials where the uncertainty is described via a l₂ ball in coefficient space. It is shown constructively that under the only assumption that all the polynomials of the family are Schur, the sought filter can be provided in closed form as a polynomial or rational function with an a-priori bounded degree. The proposed synthesis procedure is based on the solution of a simple polynomial factorization problem.