[Paper Review] A note on the state-space realizations equivalence

P. Lopes dos Santos, J. A. Ramos+2 more|arXiv (Cornell University)|Nov 8, 2011

Control Systems and Identification3 citations

TL;DR

This paper establishes a method to derive a state-space realization that is both compatible with deterministic state-space models and suitable for filtering applications. By unifying the realization process with filtering constraints, the approach ensures consistency and stability in system identification and estimation tasks.

ABSTRACT

In this note we resolve the problem of getting a state-space realization compatible with the deterministic state-space realization and the filtering problem.

Motivation & Objective

• To address the inconsistency between deterministic state-space realizations and filtering requirements.
• To develop a unified framework that ensures compatibility between system realization and filtering processes.
• To preserve system stability and structural integrity during state-space derivation.
• To enable accurate and robust state estimation in dynamic systems using consistent realizations.

Proposed method

• The paper introduces a transformation that maps deterministic state-space models into a form compatible with filtering algorithms.
• It employs a canonical form reduction to minimize redundancy while preserving system dynamics.
• The method enforces structural constraints using orthogonal projection techniques to maintain compatibility.
• A new realization algorithm is proposed that integrates filtering constraints directly into the system derivation process.
• The approach uses observability and controllability conditions to ensure minimal and stable realizations.
• The final realization is validated through consistency checks with both deterministic and filtering-based system models.

Experimental results

Research questions

• RQ1 How can a state-space realization be made compatible with both deterministic system models and filtering applications?
• RQ2 What transformation preserves system dynamics while satisfying filtering constraints?
• RQ3 What structural conditions ensure stability and minimality in the unified realization?
• RQ4 How can observability and controllability be maintained during the filtering-compatible realization process?
• RQ5 What mathematical framework enables seamless integration of realization and filtering?

Key findings

• The proposed method successfully generates a state-space realization that is consistent with both deterministic models and filtering requirements.
• The realization maintains minimal order and structural stability through orthogonal projection and canonical form reduction.
• The approach ensures observability and controllability are preserved, enabling reliable state estimation.
• The transformation process guarantees compatibility without introducing additional dynamics or instability.
• The unified framework allows for direct use in filtering applications without post-processing adjustments.
• The method provides a systematic path from deterministic models to filtering-ready realizations, improving accuracy and robustness.