Stability Analysis of Time-Delay Systems via Energy Dissipation Operators
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Abstract
This paper proposes a novel stability analysis framework for linear time-delay systems based on an energy dissipation operator (EDO), which avoids the use of Lyapunov–Krasovskii functionals and linear matrix inequalities. An operator-based stability criterion is developed and rigorously established through explicit dissipation inequalities. Explicit exponential decay-rate bounds are derived using a Razumikhin–Halanay-type analysis. The proposed framework is further extended to neutral and fractional-order time-delay systems. Numerical simulations are provided to verify the theoretical results and demonstrate the effectiveness of the proposed approach.
Manuscript received: 02 Feb 2026 | Revised: 27 Mac 2026 | Accepted: 29 Apr 2026 | Published: 31 Jul 2026
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