Abstract
In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.
Original language | English |
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Pages (from-to) | 2248-2259 |
Number of pages | 12 |
Journal | Nonlinear Analysis, Theory, Methods and Applications |
Volume | 65 |
Issue number | 12 |
DOIs | |
Publication status | Published - 2006 Dec 15 |
Externally published | Yes |
Keywords
- Activation time ratio between stable and unstable subsystems
- Arbitrary switching
- Common Lyapunov function
- Stability
- Switched normal system
ASJC Scopus subject areas
- Analysis
- Applied Mathematics