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Input-output Approach and Scaled Small Gain Theorem Analysis to Sampled-data Systems with Time-varying Delay

Ouarda Lamrabet*, El Houssaine Tissir, Nabil El Fezazi, and Fatima El Haoussi
International Journal of Control, Automation, and Systems, vol. 18, no. 9, pp.2242-2250, 2020

Abstract : This article presents some novel results on sampled-data H∞ control for a class of linear systems. The proposed system is affected by time-varying delay and external disturbance. The main goal of this paper is to transform the original system into an equivalent two interconnected subsystems through the combination of input-output approach and scaled small gain (SSG) theorem. Then, the three term approximation method is adopted to approximate the time-varying delay. By incorporating Lyapunov-Krasovskii functional and wirtinger integral inequality, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantee the stability of the closed loop system, and a H∞ norm bound performances. Finally, the applicability of the developed control design technique and its less conservativeness over other existing ones are proven by means of simulation Examples.

Keyword : H∞ control, sampled-data control, scaled small gain theorem, time-varying delay.

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