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

We consider the problem of robust stability analysis for feedback interconnections of causal linear systems that are potentially time-varying with unbounded gain over the space of finite-energy inputs. To this end, a combination of ν-gap metric and integral-quadratic-constraint based analysis is employed. The main results are developed in an abstract setting using generalized Wiener-Hopf and Hankel operators and the Fredholm index. Underlying assumptions are then verified for two important classes of system: multiplication by constantly proper Callier-Desoer transfer functions; and stabilizable and detectable finite-dimensional state-space systems with coefficients of bounded and continuous variation across time.