Optimal Finite-Time State Estimation for Discrete-Time Switched Systems under Switching Frequency Constraint

The state estimation problem for a class of switched linear systems which only switches in some short interval is addressed. Besides the asymptotic stability of error dynamics, the boundness of error state is a significant issue for short-time switched systems. By introducing the concept of finite-t...

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Bibliographic Details
Published in:Mathematical problems in engineering 2014-01, Vol.2014 (1)
Main Authors: Du, Lin, Xiang, Weiming, Zhao, Yongchi
Format: Article
Language:English
Subjects:
Asymptotic methods
Control theory
Design
Discrete time systems
Dynamical systems
Dynamics
Errors
Frequency stability
Genetic algorithms
Intervals
Iterative algorithms
Linear systems
Mathematical models
Mathematical problems
Observers
Optimization
State estimation
State observers
Switching
Systems stability
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Summary:The state estimation problem for a class of switched linear systems which only switches in some short interval is addressed. Besides the asymptotic stability of error dynamics, the boundness of error state is a significant issue for short-time switched systems. By introducing the concept of finite-time stability, the state estimation procedure is formulated to determine appropriate observer gains ensuring the error dynamics is finite-time stable in the short-time switching intervals of interest. Optimal finite-time observers are designed through iterative algorithms to minimize the bound of error state, in the cases with and without disturbances. Particularly, when the total activation time is known, a less conservative result can be derived and an optimization problem can be solved with the help of the genetic algorithm. A numerical example is provided to illustrate the theoretical findings in this paper.
ISSN:1024-123X
1563-5147
DOI:10.1155/2014/512485