A stability analysis technique called trajectory-based approach

Frédéric Mazenc (CentraleSupelec, CNRS, Paris-Saclay) Slides

We present a recent stability analysis technique for broad families of nonlinear dynamical systems. It is called ‘trajectory based approach’ and, in contrast with Lyapunov based approaches, it involves verifying certain inequalities along solutions of systems. It is especially useful when systems with delays and discontinuities are studied. We show how the technique can be used to prove results under the condition that a time-varying inequality of Halanay’s type is satisfied. We show that the technique applies to a wide range of systems, notably time-varying systems with time-varying delay, systems with impulses, and systems resulting from the design of finite-time observers.