A convex parametrization of risk-adjusted stabilizing controllers. (Q1413951)

The standard stability criterion, based on the transfer functions of a linear, time-invariant system, hence, the zero exclusion property, has to be fulfilled for every frequency and for all model parameters \(q\) in a given domain. Under the assumption that the vector \(q\) of model parameters has a given probability distribution, the following substitute problem for a robust controller design is considered: Instead of the standard stability condition in the frequency domain, it is required here that the zero exclusion property occurs at each frequency only with a prescribed small probability. This concept is studied then for special types of probability distributions of the random vector \(q\) of model parameters.