Stability Analysis for Time-Varying Systems with Delay using Linear Lyapunov Functionals and a Positive Systems Approach

Frédéric Mazenc 1, 2 Michael Malisoff 3
1 L2S - Laboratoire des signaux et systèmes
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
3 Department of Mathematics
Abstract : We prove stability of time-varying systems with delays, using linear Lyapunov functionals and positive systems, and we provide robustness of the stability with respect to multiplicative uncertainty in the vector fields. We allow cases where the delay may be unknown, and where the vector fields defining the systems are not necessarily bounded. We illustrate our work using a chain of integrators and other examples.
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Frédéric Mazenc, Michael Malisoff. Stability Analysis for Time-Varying Systems with Delay using Linear Lyapunov Functionals and a Positive Systems Approach. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2016, 61 (3), pp.771-776. ⟨10.1109/TAC.2015.2446111⟩. ⟨hal-01257336⟩

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