On convexified robust control synthesis
Since the 1990s, it is known that conditions for robust controller design with \(H_{\infty}\) performance specifications can be formulated as nonlinear matrix inequalities which are typically non-convex and hence difficult to solve numerically. These conditions can be ``convexified'' into linear matrix inequalities (LMI), using appropriate changes of variables, only in very specific cases. The main contribution of this paper is to describe a particular class of systems for which this convexification can be carried out. These systems admit a structured state-space description given by relation (12), where either the signals coming from the perturbation or uncertainty block can be fully measured, or the system state can be fully measured. This can be seen as a slight generalization of the ``full-information'' case identified previously in the robust control literature. Under these assumptions, the robust controller design procedure boils down to solving a convex LMI problem for which several numerical solvers are available. Another contribution of the paper is to show that for this particular class of systems, there is no performance improvement brought by gain-scheduling control (where the control law is dynamically updated based on on-line measurements of system parameters) over robust control (where the control law is not updated).
scientific article; zbMATH DE number 2117913