Linear-time invariant Positive Systems: Stabilization and the Servomechanism Problem

Positive systems, which carry the well known property of confining the state, output, and/or input variables to the nonnegative orphant, are of great practical importance, as the nonnegative property occurs quite frequently in numerous applications and in nature. These type of systems frequently occur in hydrology where they are used to model natural and artificial networks of reservoirs; in biology where they are used to describe the transportation, accumulation, and drainage processes of elements and compounds like hormones, glucose, insulin, and metals; and in stocking, industrial, and engineering systems where chemical reactions, heat exchanges, and distillation processes take place. The interest of this dissertation is in two key problems: positive stabilization and the positive servomechanism problem. In particular, this thesis outlines the necessary and sufficient conditions for the stabilization of positive linear time-invariant (LTI) systems using state feedback control, along with providing an algorithm for constructing such a stabilizing regulator. Moreover, the results on stabilization also encompass the two problems of the positive separation principle and stabilization via observer design. The second, and most emphasized, problem of this dissertation considers the positive servomechanism problem for both single-input single-output (SISO) and multi-input multi-output (MIMO) stable positive LTI systems. The study of the positive servomechanism problem focuses on the tracking problem of nonnegative constant reference signals for unknown/known stable SISO/MIMO positive LTI systems with nonnegative unmeasurable/measurable constant disturbances via switching tuning clamping regulators (TcR), linear quadratic clamping regulators (LTQcR), and ending with MPC control. Finally, all theoretical results on the positive servomechanism problem are justified via numerous experimental results on a waterworks system.

Department dc:contributor.department

Electrical and Computer Engineering

Year dc:date.issued

2009

Author dc:creator

• Roszak, Bartek

Advisor dc:contributor.advisor

• Davison, Edward J.

• positive systems
• positive stabilization
• positive servomechanism problem
• tracking and disturbance rejection
• tuning clamping regulators
• LQR and MPC optimal control

Statement dc:rights

• Attribution-NonCommercial-NoDerivs 2.5 Canada

Licence dc:rights.uri

• http://creativecommons.org/licenses/by-nc-nd/2.5/ca/

Language dc:language.iso

en_ca

Handle dc:identifier.uri

http://hdl.handle.net/1807/32018

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/32018