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<p>This paper presents a systematic method for representing nonlinear systems in discrete-time quasi-linear parameter-varying (quasi-LPV) canonical forms, specifically controllable and observable forms. The proposed methods directly derive the canonical state-space representations from input–output difference equations, a structure widely used in system identification, neural network architectures, and data-driven modeling paradigms. This approach differs fundamentally from classical realization theory, which is typically restricted to linear time-invariant systems. The key contributions include deriving controllable and observable canonical models with time-varying system matrices and establishing theoretical foundation based on the invariance of parameterization maps during system evolution. The practical utility of the proposed framework is demonstrated through Model Predictive Control (MPC) design for a nonlinear DC motor speed control system, where the quasi-LPV canonical models enable systematic controller synthesis. Simulation results validate the effectiveness of the proposed approach in capturing nonlinear dynamics and achieving satisfactory control performance.</p>

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On Quasi-LPV Realizations in Controllable and Observable Canonical Forms

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Deepti Khimani,
  • Machhindranath Patil,
  • Sharad Bhartiya

摘要

This paper presents a systematic method for representing nonlinear systems in discrete-time quasi-linear parameter-varying (quasi-LPV) canonical forms, specifically controllable and observable forms. The proposed methods directly derive the canonical state-space representations from input–output difference equations, a structure widely used in system identification, neural network architectures, and data-driven modeling paradigms. This approach differs fundamentally from classical realization theory, which is typically restricted to linear time-invariant systems. The key contributions include deriving controllable and observable canonical models with time-varying system matrices and establishing theoretical foundation based on the invariance of parameterization maps during system evolution. The practical utility of the proposed framework is demonstrated through Model Predictive Control (MPC) design for a nonlinear DC motor speed control system, where the quasi-LPV canonical models enable systematic controller synthesis. Simulation results validate the effectiveness of the proposed approach in capturing nonlinear dynamics and achieving satisfactory control performance.