Data based interval controller design

In control synthesis, it is important for the designer to have a set of stabilizing controllers within which performance specifications are to be attained. Typically a controller can be parametrized by its transfer function coefficients and often it is desired that these be allowed to vary in independent intervals, that is an interval controller family is desired. In this paper, we consider the problem of constructing an interval controller family that stabilizes an LTI plant. A nice feature of the solution is that the only information required is the frequency response (Nyquist/Bode) of the plant to be controlled. This data is often available for real world plants. The technique is analytical, model-free and is applicable to controllers of any order. Due to the complex nature of stabilizing regions in controller parameter space, typically non-convex and not-connected, we employ a box-like structure of controller sets centered around a nominal stabilizing controller. The result obtained here is a vertex result in conjunction with a simple phase condition. The result is extended to find a set satisfying a given performance specifications. Examples are given for illustration.