Robust Stability of Linear Time Invariant Systems Represented by an Interval Matrix Article Swipe

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Hernandez-Morales, Eduardo ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.5281/zenodo.17727039

This technical note summarizes the main results of the paper presented at the IEEE Conference on Control of Oscillations and Chaos (COC’97), where we proposed sufficient conditionsto guarantee the robust stability of linear time invariant systems represented by interval matrices. The systems considered include both continuous and discrete-time formulations, andthe uncertainty is modeled as parametric variation within a bounded interval matrix.The proposed tests are based on spectral properties of the Hermitian and Skew-Hermitianparts of the centroid and difference matrices. For continuous systems, Hurwitz stability isguaranteed if the bounda1 = 2 · λmax(H(Co)) + n · dmax < 0is satisfied. For discrete systems, Schur stability is ensured if the spectral radiusβ1 = ρ(H(Co)) + ρ(H(D)) + j · ρ(S(Co)) + j · ρ(S(D)) < 1holds.These conditions are derived using classical results such as Weyl’s theorem, Gersgorin’sdisks, and Perron’s theorem. The tests are computationally efficient and avoid the exponential complexity of vertex enumerat

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Mathematics Parametric statistics Bounded function Hermitian matrix Stability (learning theory) Robust control Applied mathematics Linear system Interval (graph theory) LTI system theory Invariant (physics) Discrete time and continuous time Exponential stability Control theory (sociology) Centroid Matrix (chemical analysis) BIBO stability Vertex (graph theory) Matrix algebra Spectral properties Matrix decomposition Schur complement Mathematical analysis

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DOI: https://doi.org/10.5281/zenodo.17727039

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Title: Robust Stability of Linear Time Invariant Systems Represented by an Interval Matrix

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Publication date: 2025-11-26

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Authors: Hernandez-Morales, Eduardo

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Concepts: Mathematics, Parametric statistics, Bounded function, Hermitian matrix, Stability (learning theory), Robust control, Applied mathematics, Linear system, Interval (graph theory), LTI system theory, Invariant (physics), Discrete time and continuous time, Exponential stability, Control theory (sociology), Centroid, Matrix (chemical analysis), BIBO stability, Vertex (graph theory), Matrix algebra, Spectral properties, Matrix decomposition, Schur complement, Mathematical analysis

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