Simultaneous stabilization with near optimal LQR performance

We consider the use of linear time-varying controllers for simultaneous stabilization and performance. We prove that for every finite set of plants, we can design a linear time-varying controller which provides not only closed loop stability, but also near optimal LQR type performance. By adding a mild nonlinearity in the form of a nonlinear delay, we end up with an improved controller which provides near optimal performance for each possible model as well as for the case when the plant changes occasionally.