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Stability analysis and controller synthesis for a class of piecewise smooth systems

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Stability analysis and controller synthesis for a class of piecewise smooth systems

Samadi, Behzad (2008) Stability analysis and controller synthesis for a class of piecewise smooth systems. PhD thesis, Concordia University.

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Abstract

This thesis deals with the analysis and synthesis of piecewise smooth (PWS) systems. In general, PWS systems are nonsmooth systems, which means their vector fields are discontinuous functions of the state vector. Dynamic behavior of nonsmooth systems is richer than smooth systems. For example, there are phenomena such as sliding modes that occur only in nonsmooth systems. In this thesis, a Lyapunov stability theorem is proved to provide the theoretical framework for the stability analysis of PWS systems. Piecewise affine (PWA) and piecewise polynomial (PWP) systems are then introduced as important subclasses of PWS systems. The objective of this thesis is to propose efficient computational controller synthesis methods for PWA and PWP systems. Three synthesis methods are presented in this thesis. The first method extends linear controllers for uncertain nonlinear systems to PWA controllers. The result is a PWA controller that maintains the performance of the linear controller while extending its region of convergence. However, the synthesis problem for the first method is formulated as a set of bilinear matrix inequalities (BMIs), which are not easy to solve. Two controller synthesis methods are then presented to formulate PWA and PWP controller synthesis as convex problems, which are numerically tractable. Finally, to address practical implementation issues, a time-delay approach to stability analysis of sampled-data PWA systems is presented. The proposed method calculates the maximum sampling time for a sampled-data PWA system consisting of a continuous-time plant and a discrete-time emulation of a continuous-time PWA state feedback controller.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical and Industrial Engineering
Item Type:Thesis (PhD)
Authors:Samadi, Behzad
Pagination:xv, 171 leaves : ill. ; 29 cm.
Institution:Concordia University
Degree Name:Ph. D.
Program:Mechanical and Industrial Engineering
Date:2008
Thesis Supervisor(s):Rodrigues, Luis
ID Code:975835
Deposited By: Concordia University Library
Deposited On:22 Jan 2013 16:15
Last Modified:18 Jan 2018 17:41
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