Exponential Stability Analysis via Integral Quadratic Constraints

Understand

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.