Robust Control of Uncertain Systems with Time-Varying Uncertainty: A Computer-Aided Setup with Illustrations

The problem of stabilising a class of linear uncertain systems by using linear state feedback is addressed. The system possesses uncertainty which is time-varying, unknown, but lies within a prescribed set (hence bounded). No statistical information of the uncertainty is imposed. Nor any match condition is required. Necessary and sufficient conditions for quadratic stabilisability are formulated. The controller synthesis and stability analysis are investigated by a two level optimisation process. The result is believed to be practical (in the sense that it can be implemented for non-trivial physical systems) and non-conservative.