<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.</p></abstract>

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems

Department of Mechanical Engineering, Osaka Prefecture University Sakai, Osaka 599-8531, Japan

Department of Electrical and Computer Engineering, Penn State Erie, Erie, PA 16563-1701, USA

Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA

Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL 60607-7053, USA

International Journal of Applied Mathematics and Computer Science

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by...

Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems

Publié en ligne: 14 mars 2009

Pages: 447 - 454

DOI: https://doi.org/10.2478/v10006-007-0036-x

Mots clés
switched systems, common quadratic Lyapunov functions, Lie algebra, exponential stability, arbitrary switching, dwell time scheme

This content is open access.

Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems

Publié en ligne: 14 mars 2009

Pages: 447 - 454

DOI: https://doi.org/10.2478/v10006-007-0036-x

Mots clésswitched systems, common quadratic Lyapunov functions, Lie algebra, exponential stability, arbitrary switching, dwell time scheme

This content is open access.

Mots clés
switched systems, common quadratic Lyapunov functions, Lie algebra, exponential stability, arbitrary switching, dwell time scheme