Robust L₂-L_∞ Controller Design of a Class of Uncertain Stochastic Systems with Wiener Process Disturbances

Abstract

The optimal L₂-L_∞ control problem of a class of uncertain stochastic systems with Wiener process disturbances is studied. Based on the robust L₂-L_∞ control theory, it gives a sufficient condition to solve the resilient controller such that the stochastic system is stochastically stabilizable and satisfies the given L₂-L_∞ control performance index. By constructing an appropriate Lyapunov-Krasovskii functional and applying linear matrix inequalities techniques, the L₂-L_∞ controller design problem is derived and then described as an optimization one. Simulation results are given to demonstrate the validity of the proposed approach.

KEYWORDS:

• L₂-L_∞ controller
• Linear matrix inequalities (LMIs)
• Lyapunov–Krasovskii functional
• Stochastic systems

Additional information

Funding

This work was financially supported by the National Science Foundation of China under [grant number 61272025], the Natural Science Foundation of Education Department of Anhui Province under [grant number KJ2017A522, KJ2018A0608], the Excellent Top-Notch Talent Cultivation Funding Project of Education Department of Anhui Province under [grant number gxbjzd57] and the Quality Project of Education Department of Anhui Province under [grant number 2017sjjd088, 2017xgkxm71].

Notes on contributors

Feng Xue

Feng Xue received the MS degree in electronic information from Anhui University School, Hefei, China in 2008. He is currently the associate professor with the School of Electronic and Electrical Engineering, Anhui Sanlian University, Hefei, China. His research interests are mainly in the signal and information processing. Tel/fax: [phone] Email: [email protected].

Hong-hai Wang

Honghai Wang received the MS degree in computer application technology from Anhui University, Hefei, China. He is currently the professor with the School of Electronic and Electrical Engineering, Anhui Sanlian University, Hefei, China. His current research interests include database and data mining and signal processing. Tel/fax: [phone] Email: [email protected].

De-xiang Zhang

Dexiang Zhang received the MS degree in pattern recognition and PhD degree in computer science from Anhui University, Hefei, China, in 2006 and 2011, respectively. He is currently the professor with the School of Electronic and Electrical Engineering, Anhui University, Hefei, China. His research interests are primarily in the area of image processing, digital signal processing and speech signal processing. Tel/fax: [phone] Corresponding author. Email: [email protected].