Robust stability of uncertain piecewise-linear systems: LMI approach

In this paper we propose sufficient conditions for the robust stability of time-invariant uncertain piecewise-linear systems using homogeneous polynomial Lyapunov functions. The proposed conditions are expressed in terms of linear matrix inequalities, which can be numerically determined. We solve th...

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Bibliographic Details
Published in:Nonlinear dynamics 2011-01, Vol.63 (1-2), p.183-192
Main Authors: BenAbdallah, Abdallah, Hammami, Mohamed Ali, Kallel, Jalel
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Control systems
Control theory
Dynamical Systems
Engineering
Liapunov functions
Linear control
Linear matrix inequalities
Linear systems
Lyapunov functions
Mathematical analysis
Matrix methods
Mechanical Engineering
Nonlinear dynamics
Original Paper
Polynomials
Robustness (mathematics)
Stability
Stabilization
Vibration
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Summary:In this paper we propose sufficient conditions for the robust stability of time-invariant uncertain piecewise-linear systems using homogeneous polynomial Lyapunov functions. The proposed conditions are expressed in terms of linear matrix inequalities, which can be numerically determined. We solve the stabilization of piecewise uncertain linear control systems by using state piecewise-linear feedback. We propose an illustrative example to show the efficiency of the proposed approach.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-010-9795-2