Extended Full Block S-Procedure for Distributed Control of Interconnected Systems

TL;DR

This paper introduces an extended Full Block S-Procedure for distributed control of interconnected systems, reducing conservatism by relaxing structural assumptions and enabling decomposition into smaller synthesis conditions.

Contribution

It extends the FBSP with additional variables, allowing less conservative distributed controller synthesis for homogeneous interconnected systems.

Findings

Reduces conservatism compared to existing methods

Enables decomposition into small, subsystem-sized conditions

Improves distributed control design flexibility

Abstract

This paper proposes a novel method for distributed controller synthesis of homogeneous interconnected systems consisting of identical subsystems. The objective of the designed controller is to minimize the L2-gain of the performance channel. The proposed method is an extended formulation of the Full Block S-Procedure (FBSP) where we introduce an additional set of variables. This allows relaxing the block-diagonal structural assumptions on the Lyapunov and multiplier matrices required for distributed control design, which reduces conservatism w.r.t most existing approaches. We show how to decompose the proposed extended FBSP into small synthesis conditions, of the size of one individual subsystem.