Decoupling Periodic Systems: An Algebraic Approach

TL;DR

This paper introduces an algebraic method for decoupling discrete-time periodic systems using nonregular state feedback, extending existing techniques to nonsquare systems with more inputs than outputs.

Contribution

It provides a novel algebraic approach for decoupling periodic systems with more inputs than outputs, including a new extension for nonsquare systems.

Findings

Algebraic decoupling method for periodic systems

Extension to nonsquare systems with more inputs than outputs

Use of nonregular state feedback for decoupling

Abstract

This paper addresses the problem of row-by-row (or diagonal) decoupling of discrete-time linear multi-input multi-output systems with periodic time-varying coefficients using periodic state feedback. Previous solutions have tackled row-by-row decoupling using dynamic compensation for square systems and block-decoupling through regular state feedback for nonsquare systems with more outputs than inputs. While it appears likely that a row-by-row state feedback solution for square systems can be deduced from these findings, a direct argument seems more appropriate here as it presents a natural extension for decoupling nonsquare systems with more inputs than outputs. This extension, which necessitates nonregular state feedback, has yet to be explored for periodic systems. Our approach is purely algebraic, based on a time-invariant representation of the periodic system.