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<p>In this paper, we develop a framework for multilinear time-invariant (MLTI) description systems based on tensor M-product and establish fundamental theoretical results. We derive necessary and sufficient conditions for regularity and stability via tensor spectral analysis and introduce new tensor-based concepts of controllability and observability via multilinear operator theory. Furthermore, we address the dynamic order assignment problem via full-state derivative feedback. In addition, we extend the optimal control problem and establish the solution for multilinear quadratic regulation. Connections to neural network system analysis are explored by analyzing the stability of tensor-based neural models using descriptor system methods. To demonstrate practical relevance, we provide illustrative examples, including applications in modeling complex motor systems and LCR circuits.</p>

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Multilinear time-invariant descriptor systems

  • 期刊论文

  • 发表日期：

    2025年5月12日

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  • Wanli Ma,
  • Chengdong Liu,
  • Yimin Wei

摘要

In this paper, we develop a framework for multilinear time-invariant (MLTI) description systems based on tensor M-product and establish fundamental theoretical results. We derive necessary and sufficient conditions for regularity and stability via tensor spectral analysis and introduce new tensor-based concepts of controllability and observability via multilinear operator theory. Furthermore, we address the dynamic order assignment problem via full-state derivative feedback. In addition, we extend the optimal control problem and establish the solution for multilinear quadratic regulation. Connections to neural network system analysis are explored by analyzing the stability of tensor-based neural models using descriptor system methods. To demonstrate practical relevance, we provide illustrative examples, including applications in modeling complex motor systems and LCR circuits.