On the State-Space Realization of LPV Input-Output Models: Practical Approaches

A common problem in the context of linear parameter-varying (LPV) systems is how input-output (IO) models can be efficiently realized in terms of state-space (SS) representations. The problem originates from the fact that in the LPV literature discrete-time identification and modeling of LPV systems...

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Bibliographic Details
Published in:IEEE transactions on control systems technology Vol. 20; no. 1; pp. 139 - 153
Main Authors: Toth, R., Abbas, H. S., Werner, H.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Approximation
Approximation error
Atmospheric modeling
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Dynamic dependence
Dynamic scheduling
Dynamical systems
Dynamics
Equivalence
Exact sciences and technology
input-output (IO) representation
linear parameter-varying (LPV) systems
Markov processes
Mathematical analysis
model reduction
Modelling and identification
Operational research and scientific management
Operational research. Management science
Polynomials
realization
Representations
Scheduling
Scheduling, sequencing
state-space (SS) representation
Studies
Trajectory
Transformations
System realization
Kalman filter
Dynamic dependence
model reduction
Linear parameter varying system
State space
Scheduling
State space method
Linear control
state-space (SS) representation
realization
Time varying system
Linear time invariant system
Instantaneous value
input-output (IO) representation
Discrete time
Approximation error
Delay time
Reduced order systems
System identification
linear parameter-varying (LPV) systems
State estimation
Input output model
ISSN:1063-6536, 1558-0865
Online Access:Get full text
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Summary:A common problem in the context of linear parameter-varying (LPV) systems is how input-output (IO) models can be efficiently realized in terms of state-space (SS) representations. The problem originates from the fact that in the LPV literature discrete-time identification and modeling of LPV systems is often accomplished via IO model structures. However, to utilize these LPV-IO models for control synthesis, commonly it is required to transform them into an equivalent SS form. In general, such a transformation is complicated due to the phenomenon of dynamic dependence (dependence of the resulting representation on time-shifted versions of the scheduling signal). This conversion problem is revisited and practically applicable approaches are suggested which result in discrete-time SS representations that have only static dependence (dependence on the instantaneous value of the scheduling signal). To circumvent complexity, a criterion is also established to decide when an linear-time invariant (LTI)-type of realization approach can be used without introducing significant approximation error. To reduce the order of the resulting SS realization, an LPV Ho-Kalman-type of model reduction approach is introduced, which, besides its simplicity, is capable of reducing even non-stable plants. The proposed approaches are illustrated by application oriented examples.
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ISSN:1063-6536
1558-0865
DOI:10.1109/TCST.2011.2109040