Matrix equations in multivariable control

Abstract

The contribution is focused on a control design and simulation of multi input output (MIMO) linear continuous-time systems. Suitable and efficient tools for description and controller derivation are algebraic notions as rings, polynomial matrices, and Diophantine equations. The generalized MIMO PI controller design is studied for stable and unstable systems. A unified approach through matrix Diophantine equation can be applied in both cases. All stabilizing feedback controllers are obtained via solutions of a matrix Diophantine equation. The methodology allows defining scalar parameters (one or more) for tuning and influencing of controller parameters. A Matlab-Simulink program implementation was developed for simulation and verification of the studied approach. Illustrative examples show the effectiveness and flexibility of the proposed method for some simple MIMO systems. © 2015 World Scientific and Engineering Academy and Society. All rights reserved.