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Stability analysis of switched systems before27Jan2012

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Abstract

Switched linear systems are an important subclass of hybrid systems and consist of a finite number of linear time-invariant systems with continuous dynamics and some switching mechanism that orchestrates between them. Dynamical systems of this class can be found in various fields of engineering applications, such as aviation technology, power electronics, automotive engineering or power generation.

One of the most important considerations in control design pertains to the stability properties the system. Even though switched system analysis has been studied extensively in the last decade, few analytical tools for stability have been developed. The most common stability tools are based on numerical optimisation that provide little insight into the stability (or instability) properties of the switched system. Analytical tools on the other hand, do not suffer from this shortcoming but are often restricted to subclasses of switched systems and require the system to be of particular structures that are often not motivated by applications but are derived from theoretical reasoning.

Our research aims to develop methods for the stability analysis of switched systems that are easily applicable in practice and support the design process of stable high-performance controllers.

Cooperations

  • Fabian Wirth, Fachbereich Mathematik und Informatik, Universität Bremen

People involved


Description

-- this page is under construction - more information will be added soon -- please contact the researchers involved for further information

Publications

Ishan Pendharkar, Kai Wulff, Jörg Raisch. On the construction of quadratically stable switched linear systems with multiple component systems. In Proceedings of the Conference on Decision and Control, 2007,
Ishan Pendharkar, Kai Wulff, Jörg Raisch. A behavioral-theoretic approach to quadratic stability of switched linear systems. In 13th IEEE IFAC International Conference on Methods and Models in Automation and Robotics, Szczecin, Poland, 2007.
Kai Wulff, Robert Shorten. On the existence of periodic motion and the maximum sector bounds for absolute stability of nonlinear nonstationary systems. In Proceedings of IX International Workshop on Stability and Oscillations of Nonlinear Control Systems, Special Issue Automation and Remote Control, 2007.
R. Shorten, F. Wirth, O. Mason, K. Wulff, C. King. Stability criteria for switched and hybrid systems. publication scheduled for Dec 2007 in SIAM review,
Kai Wulff, Robert Shorten. On maximum sector bounds for absolute stability of single-input single-output systems. International Journal of Control, 80 (6):832–842, 2007.
Kai Wulff, Fabian Wirth, Robert Shorten. On the stabilisation of a class of switched single-input single-output systems. In IEEE Conference on Decision and Control and European Control Conference, Sevilla, 2005.
Kai Wulff, Robert Shorten. A generalisation of the 45° Criterion for the stability of time-varying systems with non-real eigenvalues. In IEE Irish Signals and Systems Conference, 2005.
Robert Shorten, Oliver Mason, Kai Wulff. Switching and Learning in Feedback systems, Convex cones, Lyapunov functions, and the stability of switched linear systems, Springer-Verlag, 2004.
Robert Shorten, Paul Curran, Kai Wulff. On time-domain multiplier criteria for single-input single-output systems. @International Journal of Control, 77 (11):985–991, 2004.
Kai Wulff, John Foy, Robert Shorten. Comments on the relation of periodic and absolute stability of switched linear systems. In American Control Conference, pages 3226–3227, Denver, 2003.
Robert Shorten, Paul Curran, Kai Wulff. On time-domain multiplier criteria for single-input single-output systems. In Proceedings of 42nd Conference on Decision and Control, Hawaii, 2003.
Robert Shorten, Oliver Mason, Kai Wulff. On the existence of common quadratic Lyapunov functions for single-input single-output switched systems. In 12th Yale Workshop on Adaptive and Learning Systems, 2003.
Kai Wulff, Robert Shorten, Paul Curran. On the 45° region and the uniform asymptotic stability of classes of second order parameter varying and switched systems. @International Journal of Control, 75 (11):812-823, 2002.
Kai Wulff, Robert Shorten, Paul Curran. On the relationship of matrix-pencil eigenvalue criteria and the choice of {L}yapunov function for the analysis of second order switched systems. In American Control Conference, Anchorage, 2002.
session award
Kai Wulff, Paul Curran, Robert Shorten. On the Infinity-Norm and the Asymptotic Stability of a class of Second order Time-Varying Systems. In Proceedings of Irish Signals and Systems Conference, 2001.
best paper award, best presentation award

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