Title: Exponential Stability Analysis via Integral Quadratic Constraints,
Abstract: The theory of integral quadratic constraints (IQCs) allows verification of
stability and gain-bound properties of systems containing nonlinear or
uncertain elements. Gain bounds often imply exponential stability, but it can
be challenging to compute useful numerical bounds on the exponential decay
rate. This work presents a generalization of the classical IQC results of
Megretski and Rantzer that leads to a tractable computational procedure for
finding exponential rate certificates that are far less conservative than ones
computed from $L_2$ gain bounds alone. An expanded library of IQCs for
certifying exponential stability is also provided and the effectiveness of the
technique is demonstrated via numerical examples.