Robust stability and performance analysis using shifted quadratic and nonquadratic guaranteed cost bounds

A number of guaranteed cost bounds have been proposed for robust stability and performance. In this paper we present an extension of the bounded real bound called the shifted bounded real bound, and derive shifted extensions of several known bounds, in particular, the shifted Popov, shifted linear, and shifted inverse bounds. Finally, we obtain a minimum entropy bound which generalizes the bound in Bernstein et al. (1993).