Piecewise Linear Control Systems

This thesis treats analysis and design of piecewise linear control systems. Piecewise linear systems capture many of the most common nonlinearities in engineering systems, and they can also be used for approximation of other nonlinear systems. Several aspects of linear systems with quadratic constraints are generalized to piecewise linear systems with piecewise quadratic constraints. It is shown how uncertainty models for linear systems can be extended to piecewise linear systems, and how these extensions give insight into the classical trade-offs between fidelity and complexity of a model. Stability of piecewise linear systems is investigated using piecewise quadratic Lyapunov functions. Piecewise quadratic Lyapunov functions are much more powerful than the commonly used quadratic Lyapunov functions. It is shown how piecewise quadratic Lyapunov functions can be computed via convex optimization in terms of linear matrix inequalities. The computations are based on a compact parameterization of continuous piecewise quadratic functions and conditional analysis using the S-procedure. A unifying framework for computation of a variety of Lyapunov functions via convex optimization is established based on this parameterization. Systems with attractive sliding modes and systems with bounded regions of attraction are also treated. Dissipativity analysis and optimal control problems with piecewise quadratic cost functions are solved via convex optimization. The basic results are extended to fuzzy systems, hybrid systems and smooth nonlinear systems. It is shown how Lyapunov functions with a discontinuous dependence on the discrete state can be computed via convex optimization. An automated procedure for increasing the flexibility of the Lyapunov function candidate is suggested based on linear programming duality. A Matlab toolbox that implements several of the results derived in the thesis is presented.

Grantor dc:publisher

Department of Automatic Control, Lund Institute of Technology (LTH)

Year dc:date

1999

Author dc:creator

• Johansson, Mikael

• Control Engineering
• Piecewise quadratic functions
• Linear matrix inequalities
• Convex optimization
• Optimal control
• Performance analysis
• Piecewise linear Lyapunov functions
• Piecewise quadratic Lyapunov functions
• Quadratic stability
• Lyapunov stability
• Piecewise linear systems
• Nonlinear systems
• Fuzzy systems
• Hybrid systems.
• Automation
• robotics
• Automatiska system
• robotteknik
• reglerteknik

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Repository record dc:identifier

https://lup.lub.lu.se/record/19355

OAI identifier oai:identifier

oai:lup.lub.lu.se:87eefd7f-6d0f-4dbf-8546-949a2d8fc0f7