Stability and Robust H∞ Control for Time-Delayed Systems with Parameter Uncertainties and Stochastic Disturbances

• Kim, Ki-Hoon (School of Electrical Engineering, Chungbuk National University) ;
• Park, Myeong-Jin (School of Electrical Engineering, Chungbuk National University) ;
• Kwon, Oh-Min (School of Electrical Engineering, Chungbuk National University) ;
• Lee, Sang-Moon (School of Electronics Engineering, Daegu University) ;
• Cha, Eun-Jong (Department of Biomedical Engineering, School of Medicine, Chungbuk National University)
• Accepted : 2015.09.01
• Published : 2016.01.01
• 81 18

Abstract

This paper investigates the problem of stability analysis and robust H controller for time-delayed systems with parameter uncertainties and stochastic disturbances. It is assumed parameter uncertainties are norm bounded and mean and variance for disturbances of them are known. Firstly, by constructing a newly augmented Lyapunov-Krasovskii functional, a stability criterion for nominal systems with time-varying delays is derived in terms of linear matrix inequalities (LMIs). Secondly, based on the result of stability analysis, a new controller design method is proposed for the nominal form of the systems. Finally, the proposed method is extended to the problem of robust H controller design for a time-delayed system with parameter uncertainties and stochastic disturbances. To show the validity and effectiveness of the presented criteria, three examples are included.

Keywords

Stochastic disturbances;Parameter uncertainties;Time-varying delays;Lyapunov method

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