Stability of a class of linear switching systems with time delay
- 13 February 2006
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuits and Systems I: Regular Papers
- Vol. 53 (2), 384-393
- https://doi.org/10.1109/tcsi.2005.856666
Abstract
We consider a switching system composed of a finite number of linear delay differential equations (DDEs). It has been shown that the stability of a switching system composed of a finite number of linear ordinary differential equations (ODEs) may be achieved by using a common Lyapunov function method switching rule. We modify this switching rule for ODE systems to a common Lyapunov functional method switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati-type Lyapunov functional under a condition on the time delay.Keywords
This publication has 21 references indexed in Scilit:
- Sliding mode control of TDS via functional surfacesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Uniform asymptotic stability of hybrid dynamical systems with delayIEEE Transactions on Automatic Control, 2003
- Dynamics of Controlled Mechanical Systems with Delayed FeedbackPublished by Springer Science and Business Media LLC ,2002
- Stability of some linear systems with delaysIEEE Transactions on Automatic Control, 1999
- Computation of piecewise quadratic Lyapunov functions for hybrid systemsIEEE Transactions on Automatic Control, 1998
- Multiple Lyapunov functions and other analysis tools for switched and hybrid systemsIEEE Transactions on Automatic Control, 1998
- Switched Controller Synthesis for the Quadratic Stabilisation of a Pair of Unstable Linear SystemsEuropean Journal of Control, 1998
- A unified framework for hybrid control: model and optimal control theoryIEEE Transactions on Automatic Control, 1998
- Smart cars on smart roads: problems of controlIEEE Transactions on Automatic Control, 1993
- Introduction to Functional Differential EquationsApplied Mathematical Sciences, 1993