Chang Transformation for Decoupling of Singularly Perturbed Linear Time-Varying Systems

Chang Transformation for Decoupling of Singularly Perturbed Linear Time-Varying Systems

This technical note extends the decoupling method for singularly perturbed systems, Chang transformation, from linear slowly time-varying systems to linear time-varying systems with semi-proper (self-commutative) fast subsystems through the constructions of contraction mappings when negative real pa...

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Veröffentlicht in:IEEE transactions on automatic control 2016-06, Vol.61 (6), p.1637-1642
Hauptverfasser: Xiaojing Yang, Zhu, J. Jim
Format: Artikel
Sprache:eng
Schlagworte:
Approximation methods
Chang Transformation
Control theory
Decoupling
Differential equations
Eigenvalues and eigenfunctions
Integral equations
Linear systems
Linear Time-Varying System
MacLaurin series
Mathematical analysis
Riccati equation
Semi-Proper System
Singular Perturbation
Stability analysis
Time-varying systems
Transformations
Transformations (mathematics)
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Beschreibung
Zusammenfassung:This technical note extends the decoupling method for singularly perturbed systems, Chang transformation, from linear slowly time-varying systems to linear time-varying systems with semi-proper (self-commutative) fast subsystems through the constructions of contraction mappings when negative real parts of the parallel differential-eigenvalues are used to guarantee the exponential stability of the perturbed systems. MacLaurin series forms and iterative solutions in an interval of the singular perturbation parameter for the differential Riccati equation and the differential Sylvester equation are provided, which are key steps for the Chang transformation construction.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2015.2479317