This talk investigates the instability measure of linear systems defined as the sum of the unstable eigenvalues in the continuous-time case and the product of the unstable eigenvalues in the discrete-time case, which represents a key index in control with communications constraints. The problem consists of determining the largest instability measure in systems depending polynomially on parameters constrained in a semi-algebraic set. It is shown that upper bounds of the sought measure can be established via linear matrix inequality feasibility tests. Moreover, a priori and a posteriori conditions for establishing non-conservatism are proposed. Finally, two special cases of the proposed methodology are investigated: the first one concerns systems with a single parameter, and the second one concerns the determination of the largest spectral abscissa and radius.
Graziano Chesi received the Laurea from the University of Florence in 1997 and the Ph.D. from the University of Bologna in 2001. He joined the University of Siena in 2000 and the University of Hong Kong in 2006. Dr. Chesi served as Associate Editor for Automatica, the European Journal of Control, the IEEE Transactions on Automatic Control, the IEEE Transactions on Computational Biology and Bioinformatics, and Systems and Control Letters. He founded and served as chair of the Technical Committee on Systems with Uncertainty of the IEEE Control Systems Society. He served as chair of the Best Student Paper Award Committees for the IEEE Conference on Decision and Control and the IEEE Multi-Conference on Systems and Control. Dr. Chesi is author of the books “Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems” (Springer 2009) and “Domain of Attraction: Analysis and Control via SOS Programming” (Springer 2011). He is first author in more than 160 publications. He is a Fellow of the IEEE.