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<p>This paper addresses observer design for continuous-time linear systems affected by unknown disturbances. A unified framework is developed for asymptotic estimation of a prescribed linear transformation of the state using input–output measurements only. The analysis covers finite-duration perturbations, exponentially decaying disturbances, and disturbances constrained within bounded polytopic sets. For each scenario, explicit algebraic conditions guaranteeing convergence of the estimation error are derived. A derivative-based observer structure is introduced to achieve exact disturbance decoupling under polytopic constraints. The proposed approach provides constructive gain selection procedures applicable to both full-state and functional observers without reliance on optimization techniques. Numerical simulations illustrate the theoretical results.</p>

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Unified observer design for continuous-time linear systems under structured disturbances

  • 期刊论文

  • 发表日期：

    2026年5月17日

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  • Amine El Bhih,
  • Mostafa Rachik

摘要

This paper addresses observer design for continuous-time linear systems affected by unknown disturbances. A unified framework is developed for asymptotic estimation of a prescribed linear transformation of the state using input–output measurements only. The analysis covers finite-duration perturbations, exponentially decaying disturbances, and disturbances constrained within bounded polytopic sets. For each scenario, explicit algebraic conditions guaranteeing convergence of the estimation error are derived. A derivative-based observer structure is introduced to achieve exact disturbance decoupling under polytopic constraints. The proposed approach provides constructive gain selection procedures applicable to both full-state and functional observers without reliance on optimization techniques. Numerical simulations illustrate the theoretical results.