Robust controller synthesis with parameter-dependent Lyapunov variables: A dilated LMI approach

This paper enhances our previous results on dilated LMI's so that we can address robust controller synthesis problems for continuous-time LTI systems subject to real polytopic uncertainties. The replacement of a constant scalar involved in the previous dilated LMI's by an adjustable parameter is the key to accomplish this extension. The particular form of the extension enables the use of parameter-dependent Lyapunov variables in such a sound way that an advantage of the dilated LMI approach is ensured explicitly in attacking such robust controller synthesis problems. Namely, the dilated LMI approach is shown to achieve better (no worse) results than the conventional one which is restricted to parameter-independent Lyapunov variables, provided that the adjustable parameter is taken to meet a certain simple condition.