A unified framework for input-to-state stability in systems with two time scales

2003/09/01 by A.R. Teel, Andrew R. Teel, L. Moreau +2 · 232 citations
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Computer science #Control theory (sociology) #Generality #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Perturbation (astronomy) #Physics #Probabilistic and Robust Engineering Design #Robustness (evolution) #Singular perturbation #stochastic dynamics and bifurcation

paper · doi:10.1109/tac.2003.816966

published in IEEE Transactions on Automatic Control 48(9), 1526-1544 (Institute of Electrical and Electronics Engineers)

openalex publication_date 2003/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper develops a unified framework for studying robustness of the input-to-state stability (ISS) property and presents new results on robustness of ISS to slowly varying parameters, to rapidly varying signals, and to generalized singular perturbations. The common feature in these problems is a time-scale separation between slow and fast variables which permits the definition of a boundary layer system like in classical singular perturbation theory. To address various robustness problems simultaneously, the asymptotic behavior of the boundary layer is allowed to be complex and it generates an average for the derivative of the slow state variables. The main results establish that if the boundary layer and averaged systems are ISS then the ISS bounds also hold for the actual system with an offset that converges to zero with the parameter that characterizes the separation of time-scales. The generality of the framework is illustrated by making connection to various classical two time-scale problems and suggesting extensions.

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