Parametric Lyapunov Equation Approach for Robust H2 Analysis and Structured H2 Control Problems

This paper presents a new framework to deal with robust H2 analysis and structured H2 control problems for linear time-invariant multi-parameter dependent systems. These two problems still hold a special place for practical reasons and will be formulated, in the current paper, as a problem of finding an exact solution of some parametric Lyapunov equation. Two results are then proposed: i) A direct inversion method of a particular type parameter-dependent matrix. ii) A Discrete Fourier Transform (DFT) based inversion method for polynomial parameter dependent matrices. Some didactic examples are given, throughout the paper, to illustrate the validity of the proposed results.