Standard H ∞ State-Space Solution by Youla Parameterization

Abstract

In this paper, we propose one methodology to parameterize all stabilizing controllers from the central controller. This is performed using the so called “constrained doubly coprime factorization” for the constrained plant obtained from H ∞ norm constraint and central controller. The constrained left and right coprime factors are obtained by Bezout Identity, and these are used to provide Youla parameterization in which H ∞ norm of closed-loop transfer matrix can be smaller than any prescribed value. This result shows the connection between two different method of standard state-space H ∞ solution by inner function and Youla parameterization by constrained doubly coprime factorization.