Observer-based stabilization of discrete time-delay systems

• Published in: IFAC-PapersOnLine Vol. 57; pp. 43 - 48
• Main Authors: Deepak, V. Dev, Arun, N.K., Shihabudheen, K.V., Nandi M, Ankita
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2024
• Subjects: Discrete time-delay systems; Linear Matrix Inequality (LMI); Lyapunov-Krasovskii functionals (LKF); Linear Matrix Inequality (LMI); Lyapunov-Krasovskii functionals (LKF); Discrete time-delay systems
• ISSN: 2405-8963; 2405-8963
• DOI: 10.1016/j.ifacol.2024.05.008

The objective of this paper is to design an observer-based stabilizing controller for a discrete time-delay system with unmeasurable states. This study proposes a novel Lyapunov-Krasovskii (LK) functional to establish delay-dependent stabilization of a discrete time-delay system and the observer-based design is exploited to deal with the unmeasurable states of the system. To establish less conservative stabilization conditions in terms of LMIs, the reciprocally convex inequality and summation inequality are exploited. The relevance of the proposed stabilizing controller is illustrated with numerical examples.