Descriptor LQ Robust LQ Controller Design for Systems with Structured Uncertainty using Descriptor Form Representation

This paper introduced a new design method of Robust LQ regulator, which avoids the inversion of an inertia matrix allowing to use the fullstructure information of structured time-varying parameter uncertainties. The differential equation of system is expressed as a descriptor form to reserve the structure information of parameter uncertainties. Left-hand side matrix that has the uncertain parameters of inertia matrix is assumed to be Polytopic, and right-hand side matrices that include other uncertain parameters are treated as scaled small gain techniques such as μ -Synthesis. For stability, the notion of quadratic stability, using a single Lyapunov function, is used. A set of conditions, under which the problem becomes convex, can be solved through finite-dimensional convex programming.