Stability of discrete-time networked control systems and its extension for robust H _∞ control

Abstract

The stability of discrete-time Networked Control Systems (NCSs) is studied in this article. By introducing some scalars into matrix cross-term bounding technique, we present a new approach for the state feedback controller, with less conservatism, based on the Bilinear Matrix Inequalities (BMIs) and the descriptor model transformation. We further extend the method to robust H _∞ control considering both disturbances and parametric uncertainties. For the BMI problem which is difficult to be solved directly, a modified optimisation algorithm is proposed. The practicability, less conservatism and effectiveness of the results are demonstrated by two examples.

Keywords:

• networked control systems
• Lyapunov method
• descriptor model transformation
• bilinear matrix inequalities
• robust H _∞ control

Acknowledgements

This work is supported by the National Nature Science Foundation of China (NSFC, Grant nos 60934007, 60921003, 61074176), and the Grant for State Key Program for Basic Research of China (nos 973, 2007CB311006).