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Analysis and Synthesis of Nonuniformly Sampled Systems Open Access


Other title
Linear matrix inequalities
Robust stability
Nonuniform sampling
Sampled-data control
Type of item
Degree grantor
University of Alberta
Author or creator
Mustafa, Ghulam
Supervisor and department
Chen, Tongwen (Electrical and Computer Engineering)
Examining committee member and department
Tavakoli, Mahdi (Electrical and Computer Engineering)
Zhao, Qing (Electrical and Computer Engineering)
Dubljevic, Stevan (Chemical and Materials Engineering)
Mintchev, Martin (Electrical and Computer Engineering, University of Calgary)
Chen, Tongwen (Electrical and Computer Engineering)
Department of Electrical and Computer Engineering
Control Systems
Date accepted
Graduation date
Doctor of Philosophy
Degree level
Sampled-data control theory is the mathematical foundation required for the analysis and design of sampled-data systems. An important assumption in the development of conventional sampled-data control theory is that measurement sampling periods are uniform. However, with the widespread use of networked and embedded control systems it is not possible or practically feasible to have constant measurement sampling periods. Consequently, the conventional sampled-data theory needs to be re-evaluated before designing this class of control systems. Motivated by this, this thesis develops mathematical approaches for the analysis and synthesis of sampled-data systems with nonuniform sampling periods. Two types of variations in sampling period are considered. For the first type, we assume that the measurement is sampled irregularly but the input is updated regularly. For the second type, we assume that both measurement sampling and input updating occur synchronously but with nonuniform intervals. These timing models are general enough to capture many different types of variations in sampling periods. Both state estimation and control problems are considered. For state estimation, two types of filters are developed: a sampling period dependent for the first type of variations and a robust one for the second type of variations. A novel Markov model of the irregular sampling process together with the theory of Markovian jump systems lead to the design of the first type of filter. The second filter is designed by modelling the nonuniform sampling system as uncertain feedback system with linear fractional transformation uncertainty. For the control problem, a dynamic robustly stabilizing output feedback controller and a robust H-infinity controller are developed. Both controllers are designed for the second type of variations in sampling period and analysis is based on modelling the nonuniform sampling system as uncertain feedback system. All theoretical development in this thesis is in discrete time and design conditions are formulated as linear matrix inequalities (LMI's). Many solvers, such as the LMI toolbox of MATLAB, exist and can solve these convex optimization problems very efficiently. Most constant-parameter filters or controllers designed are easily implemented. The effectiveness of the proposed filters or controllers is demonstrated using simulation results.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
G. Mustafa and T. Chen. H-infinity filtering for nonuniformly sampled systems. In 23rd Canadian Conference on Electrical and Computer Engineering (CCECE), IEEE, 2010.G. Mustafa and T. Chen. H-infinity filtering for nonuniformly sampled systems: A markovian jump systems approach. Systems and Control Letters, 60(10):871- 876, 2011.G. Mustafa and T. Chen. Stabilization of non-uniformly sampled-data systems via dynamic output feedback control. Submitted for publication in IET Control Theory Appl., 2012.G. Mustafa, T. Chen, and H. Fujioka. Robust H-infinity filtering for nonuniformly sampled systems. In Proc. 50th IEEE CDC and European Control Conf., pages 1269 -1273, 2011.G. Mustafa, T. Chen, and H. Fujioka. Robust H-infinity filter design for nonuni- formly sampled systems. In Li Qiu, Jie Chen, Tetsuya Iwasaki, and Hisaya Fujioka, editors, Developments in Control Theory Towards Glocal Control, volume 76 of Control Engineering, chapter 3, pages 17-26. Inst of Engineering and Technology, 2012.

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File title: Analysis and Synthesis of Nonuniformly Sampled Systems
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