Unconstrained Parametrizations of Discrete-Time Linear InputOutput Models: Stability and Dissipativity by Construction

• 成果类型: Article
• 署名作者: Kon, Johan; Toth, Roland; van de Wijdeven, Jeroen; Heertjes, Marcel; Oomen, Tom
• 署名单位: Eindhoven University of Technology; Eindhoven University of Technology; HUN-REN; HUN-REN Institute for Computer Science & Control; ASML Holding; Delft University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3616268
• 发表日期: 2026
• 关键词: identification; systems

摘要

It is often required that identified models exhibit certain stability and dissipativity properties, e.g., passivity or & ell;(2)-gain. The aim of this article is to develop an unconstrained parametrization of linear parameter-varying (LPV) input-output (IO) discrete-time (DT) models that guarantees stability/dissipativity by construction, i.e., the model is stable/dissipative for any choice of model parameters. To achieve this, it is shown that any quadratically stable/dissipative DT-LPV-IO model can be generated by a mapping of transformed coefficient functions that are constrained to the unit ball. The unit ball is reparameterized through a Cayley transformation, resulting in a fully unconstrained parameterization. These results immediately apply to linear time-varying IO models. In the linear time-invariant case, an unconstrained parameterization of all stable/dissipative DT transfer functions is obtained. The unconstrained parametrization enables, among others, the use of neural network coefficient functions in LPV system identification while guaranteeing stability and dissipativity.