Guaranteeing Stability in Structured Input-Output Models
With Application to System Identification
Johan Kon (Eindhoven University of Technology)
Roland Toth (Eindhoven University of Technology, HUN-REN Institute for Computer Science and Control)
Jeroen Van De Wijdeven (ASML)
Marcel Heertjes (Eindhoven University of Technology, ASML)
T. Oomen (TU Delft - Team Jan-Willem van Wingerden, Eindhoven University of Technology)
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Abstract
Identifying structured discrete-time linear time/parameter-varying (LPV) input-output (IO) models with global stability guarantees is a challenging problem since stability for such models is only implicitly defined through the solution of matrix inequalities (MI) in terms of the model's coefficient functions. In this letter, a structured linear IO model class is developed that results in a quadratically stable model for any choice of coefficient functions, enabling identification using standard optimization routines while guaranteeing stability. This is achieved through transforming the MI-based stability constraints in a necessary and sufficient manner, such that for any choice of transformed coefficient functions the MIs are satisfied. The developed stable LPV-IO model is employed in simulation to estimate the parameter-varying damping of mass-damper-spring system with stability guarantees, while a standard LPV-IO model results in an unstable estimate.