Fabian Wirth
Parameter Dependent Extremal Norms for Linear Parameter Varying Systems.
Conference Proceedings: Proc. Symposium on Mathematical Theory of Networks and Systems MTNS-2002, South Bend, IN, US, 2002.
MSC:
34D08 Ordinary Differential Equations: Lyapunov exponents
93D20 Control systems, asymptotic stability
Abstract:
We study families of time-varying linear systems with restrictions on the derivative of the parameter variation. This includes the systems usually considered in the area of linear parameter varying (LPV) systems. We show that it is possible to construct exact parameterized Lyapunov norms for a wide class of such systems. This may be used to derive (locally Lipschitz) continuous dependence of the exponential growth rate on the systems data. Furthermore, it is shown that the exponential growth rate may be approximated by exponential growth rates of periodic parameter variations.

Keywords: Linear parameter-varying systems, exponential growth, extremal norms, parameter dependent Lyapunov functions, irreducibility

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Home Fabian Wirth's publication page Research Group "Regelungssysteme"
Zentrum für Technomathematik (German)
Institute for Dynamical Systems
The Maths Department
The University of Bremen

Notes:
submitted