Efficient computational methods for robustness analysis

Issues of robust stability and performance have dominated the field of systems and control theory because of their practical importance. The recently developed Integral Quadratic Constraint (IQC) based analysis method provides a framework for systematically checking robustness properties of large complex dynamical systems. In IQC analysis, the system to be analyzed is represented as a nominal, Linear Time-Invariant (LTI) subsystem interconnected with a perturbation term. The perturbation is characterized in terms of IQCs. The robustness condition is expressed as a feasibility problem which can be solved using interiorpoint algorithms. Although the systems to be analyzed have nominal LTI subsystems in many applications, this is not always the case. A typical example is the problem of robustness analysis of the oscillatory behavior of nonlinear systems, where the nominal subsystem is generally Linear Periodically Time-Varying (LPTV). The objective of the first part of this thesis is to develop new techniques for robustness analysis of LPTV systems. Two different approaches are proposed. In the first approach, the harmonic terms of the LPTV nominal model are extracted, and the system is transformed into the standard setup for robustness analysis. Robustness analysis is then performed on the transformed system based on the IQC analysis method. In the second approach, we allow the nominal system to remain periodic, and we extend the IQC analysis method to include the case where the nominal system is periodically time-varying.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2002

Author dc:creator

• Kao, Chung-Yao, 1972-

Advisor dc:contributor.advisor

• Alexandre Megretski.

• Mechanical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/29258

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/29258