SCO colloquium: Henk van Waarde

Title: In LMIs We Trust

 

Abstract: Problems encountered in Systems and Control are often considered “solved” once they have been reformulated as linear matrix inequalities (LMIs). Indeed, the conventional wisdom is that LMIs can be solved using interior point methods, for which existing software packages are readily available. Some hands-on experience, however, shows that LMI solvers can be numerically unstable. Computation time also does not scale well with the number of unknowns. At the same time, the usual suspects of LMIs (arising e.g. in Lyapunov and dissipativity theory) have a particular structure that could be exploited by specialised solvers. In this talk, we take a closer look at an LMI that arises in data-driven stabilization. As a preliminary result, we will discuss a simple iterative algorithm to solve this LMI.