Overview
ABSTRACT
This article attempts to show how the theory of dynamic systems provides, on one hand, some very useful tools for synthesizing stabilizing controllers (perturbation theory, hierarchical control, Lyapunov synthesis) and, on the other, a valuable theoretical guide for analyzing the stability and robustness of non-linear closed-loop systems (stability in the Lyapunov sense, bifurcations, Poincaré-Bendixson theorem for flat systems, averaging). The scope has been restricted to the stabilization of equilibrium points, but similar methods make it possible to treat the stabilization around other types of trajectories such as periodic orbits.
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Read the articleAUTHORS
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Jean LÉVINE : Mines Paris Tech, Automation and Systems Center
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Pierre ROUCHON : Mines Paris Tech, Automation and Systems Center
INTRODUCTION
In this issue, we will attempt to show how dynamical systems theory provides, on the one hand, very useful tools for the synthesis of stabilizing controllers (perturbation theory, hierarchical control, Lyapunov synthesis) and, on the other hand, a valuable theoretical guide for analyzing the stability and robustness of nonlinear closed-loop systems (stability in the Lyapunov sense, bifurcations, Poincaré-Bendixon theory for planar systems, averaging).
We have restricted our focus to the stabilization of equilibrium points, but similar methods can be used to stabilize other types of trajectories, such as periodic orbits.
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Dynamic systems and control
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