Graziano Chesi (University of Hong Kong)
Topological Entropy in Uncertain Networked Control Systems
Measuring the topological entropy is a key problem in networked control systems. This talk considers systems affected by structured uncertainty, and addresses the computation of the worst-case entropy defined by the largest sum of the real parts (continuous-time) or the largest product of the magnitudes (discrete-time) of the unstable eigenvalues over the admissible uncertainties. It is supposed that the coefficients of the system are polynomial functions of an uncertain vector constrained into a semi-algebraic set. It is shown that a sufficient condition for establishing an upper bound of the worst-case entropy can be given in terms of an LMI feasibility test by exploiting SOS matrix polynomials. Moreover, it is shown that under mild assumptions this condition is also necessary by using polynomials of degree sufficiently large. Lastly, a sufficient and necessary condition is presented for establishing the optimality of the computed upper bounds.