H_∞ sampled data control of systems with time-delays

Abstract

Sampled-data H _∞ control of linear systems with constant state, control and measurement delays is considered. The sampling of the controlled input and of the measured output is not assumed to be uniform. The system is modelled as a continuous-time one, where the controlled input and the measurement output have piecewise-continuous delays. The input–output approach to stability and L ₂-gain analysis is applied to the resulting system. The discretised Lyapunov functional method is extended to the case of multiple delays, where the Lyapunov functional is complete in one of the delays (in the state) and is simple in the other delays (those in the input and in the output), which are constant. Solutions to the state-feedback and the output-feedback H _∞ control problems are derived in terms of linear matrix inequalities (LMIs).

Keywords:

• sampled data control
• H _∞ control
• time-delay
• discretised Lyapunov functional
• LMI

Acknowledgements

This work was partially supported by Kamea Fund of Isreal and by C&M Maus Chair at Tel Aviv University.