A Convex Method for the Parametric Insensitive H2 Control Problem

Contrary to the standard H2 problem, the so-called insensitive H2 problem makes use of a criterion that takes explicitly into account the parametric sensitivity of the closed loop system. This problem has already been re-formulated as a structured H2 problem that is known to be equivalent to a specific BMI optimization problem when assuming with full order controller. This paper presents a new formulation leading to a convex optimization problem. This is obtained thanks to the Youla parameterization and using the specific structure of the problem. The use of a finite dimensioned orthonormal basis for the structured Youla parameter leads to an LMI-based algorithm solving the insensitive H2 problem. Its interest is shown by comparison with existing algorithms.