We consider the effect of parametric uncertainty on properties of Linear Time Invariant systems. Traditional approaches to this problem determine the worst-case gains of the system over the uncertainty set. Whilst such approaches are computationally tractable, the upper bound obtained is not necessarily informative in terms of assessing the influence of the parameters on the system performance. We present theoretical results that lead to simple, convex algorithms producing parametric bounds on the $mathcal{L}_2$-induced input-to-output and state-to-output gains as a function of the uncertain parameters. These bounds provide quantitative information about how the uncertainty affects the system.
SOSTOOLS v3.00 is the latest release of the freely available MATLAB toolbox for formulating and solving sum of squares (SOS) optimization problems. Such problems arise naturally in the analysis and control of nonlinear dynamical systems, but also in other areas such as combinatorial optimization. Highlights of the new release include the ability to create polynomial matrices and formulate polynomial matrix inequalities, compatibility with MuPAD, the new MATLAB symbolic engine, as well as the multipoly toolbox v2.01. SOSTOOLS v3.00 can interface with five semidefinite programming solvers, and includes ten demonstration examples.
