Robust stability analysis for feedback interconnections of time-varying linear systems

Abstract

Feedback interconnections of causal linear systems are studied in a continuous-time setting. The developments include a linear time-varying (LTV) generalization of Vinnicombe's ?-gap metric and an integral-quadratic- constraint-based robust L2-stability theorem for uncertain feedback interconnections of potentially open-loop unstable systems. These main results are established in terms of Toeplitz-Wiener-Hopf and Hankel operators, and the Fredholm index, for a class of causal linear systems with the following attributes: (i) a system graph (i.e., subspace of L2 input-output pairs) admits normalized strong right (i.e., image) and left (i.e., kernel) representations, and (ii) the corresponding..