Conic S-Procedure And Constrained Dissipativity

TL;DR

This paper introduces a novel version of the classical S-procedure using matrix duality and Lagrange multipliers, extending its application to systems with matrix inequality constraints for analyzing constrained dissipativity.

Contribution

It proposes a new S-procedure based on matrix duality, providing a new proof and extending results on frequency domain inequalities and constrained dissipativity.

Findings

Extended S-procedure to matrix inequality constraints

Established equivalence between frequency domain inequalities and constrained dissipativity

Provided new proof of recent results in system theory

Abstract

A new version of classical S-procedure in system theory is proposed based on duality in the space of positive definite matrices and introduction of matrix Lagrange multipliers. A new proof and extension of the recent results of T.Iwasaki, S. Hara, A. Fradkov ( Systems & Control Letters, 2005. Vol 54 (7), pp 681-691) concerning equivalence between frequency domain inequality on finite frequency range and constrained dissipativity property for linear systems is given. The results of this paper extend S-procedure to allow for analysis and design of systems with matrix inequalities constraints.