New dilated LMI characterizations for continuous-time multiobjective controller synthesis
The authors' main objective is to extend to the continuous-time case a linear matrix inequality (LMI) stabilizability condition originally available in the discrete-time case only. The main feature of the LMI condition is a decoupling between Lyapunov variables (ensuring stability or performance) and controller variables. The extension proposed in this paper is only partial and incomplete, but covers a non-trivial multiobjective design problem mixing \(H_2\) performance and pole location in a given region. It is shown that this design problem can be formulated as a nonlinear matrix inequality. This matrix inequality is non-convex in general, but it becomes a convex LMI problem when fixing a scalar parameter. Interestingly, it is shown in Theorem 6 that this LMI is always less conservative than previously available LMI design conditions, irrespective of the choice of the scalar parameter. This is the main contribution of this technical communique.
scientific article; zbMATH DE number 2137230