On Observer-Based Control of One-Sided Lipschitz ω-Tempered Fractional-Order Systems under Input Saturation

Abstract

This paper addresses the critical challenge of observer-based control for one-sided Lipschitz (OSL) nonlinear systems governed by tempered fractional-order dynamics under input saturation constraints. We introduce a novel stability framework combining ω-tempered Caputo derivatives with Mittag-Leffler stability theory, enabling significantly faster exponential error decay compared to classical fractional operators. The proposed methodology features three key innovations: (1) a tempered Mittag-Leffler stability theorem incorporating sector-bounded saturation nonlinearities, (2) linear matrix inequality (LMI) conditions accommodating arbitrary OSL constants (ρ∈ R), and (3) a Cone Complementary Linearization (CCL) algorithm resolving gain synthesis challenges in tempered fractional systems. Numerical validation demonstrates 62% faster convergence than classical fractional approaches while maintaining saturation constraints. The CCL algorithm provides guaranteed convergence with computational efficiency, overcoming initialization sensitivity through regularization techniques.OPEN ACCESS Received: 05/06/2025 Accepted: 15/08/2025 Published: 27/10/2025

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