Linear Matrix Inequalities in Control

Many standard control problems can be formulated as linear matrix inequalities (LMIs) such as the H2-state-feedback control problem and can be efficiently solved as a convex optimisation problem by means of freely available software, for instance, by using the LMI solver SeDuMi and the LMI parser YALMIP. An important characteristic of convex optimisation on an LMI problem is that a global optimum can be found numerically if it exists even if there is no analytical solution to the LMI problem in general. Numerically, very efficient algorithms for solving optimisation problems over LMIs are based on the so-called interior point method, which converts a constrained problem to an unconstrained one by means of a barrier function.