Towards tractable off-line robustified controllers for uncertain systems

This paper proposes an off-line procedure which enables the robustification of an initial stabilizing controller for multivariable systems using the convex optimization of a Youla parameter. This robustification must provide stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Solving this problem leads to verify a Bilinear Matrix Inequality (BMI) for each vertex of the polytopic domain. To overcome the problem faced with BMIs, an alternative tractable sub-optimal solution is proposed, based on the minimization of the complementary sensitivity function permitting to enlarge the stability domain. To illustrate the potential of the developed method, an application to a simplified model of a stirred tank reactor is further examined.