SOSTOOLS and its control applications

In this chapter we present SOSTOOLS, a third-party MATLAB toolbox for formulating and solving sum of squares optimization problems. Sum of squares optimization forms a basis for formulating convex relaxations to computationally hard problems such as some that appear in systems and control. Currently, sum of squares programs are solved by casting them as semidefinite programs, which can in turn be solved using interior-point based numerical methods. SOSTOOLS helps this translation in such a way that the underlying computations are abstracted from the user. Here we give a brief description of the toolbox, its features and capabilities (with emphasis on the recently added ones), as well as show how it can be applied to solving problems of interest in systems and control.