Improved Results on L2-L∞ Performance Analysis for Additive Time-Delay Systems having Norm-Bounded Uncertain Components

Soundararajan G. Karthik C. Kashkynbayev A. Nagamani G.
December 2025 Birkhauser

Qualitative Theory of Dynamical Systems
2025 #24 Issue 6

This paper focuses on the analysis of L2-L∞ performance for a class of linear systems which includes the time-varying uncertain parameters and additive delay components. A basic state-feedback controller is designed to overcome the arduous induced by the norm-bounded uncertainties involved in the plant. With the framework of linear matrix inequality (LMI) and the theory of Lyapunov stability analysis, several sufficient conditions are proposed that ensure L2-L∞ performance and stabilization criterion of uncertain linear additive time-delay systems are proposed. This report goes beyond the existing literature by extending basic results on robust performance analysis to time-delay systems with additive delay factors, using the relaxed-based integral inequality (RII). The correctness and advantages of these theoretical records are verified by some numerical examples along with their diagrammatic visualization.

L₂-L_∞ performance , Linear matrix inequality , Lyapunov-Krasovskii functional , Relaxed-based integral inequality , State-feedback control

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Department of Mathematics, Nazarbayev University, Astana, 010000, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology (Deemed to be University), Kattankulathur, Chennai, 603203, India
Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Dindigul, 624302, India

Department of Mathematics
Institute of Mathematics and Mathematical Modeling
Department of Mathematics
Department of Mathematics

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