Guaranteeing Stability in Structured Input-Output Models: With Application to System Identification

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.