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Contraction theory provides an elegant way to analyze the behaviors of certain nonlinear dynamical systems. Under sometimes easy to check hypotheses, systems can be shown to have the incremental stability property that trajectories converge to each other.
This website provides a tutorial overview of contraction theory for nonlinear stability analysis and control synthesis of deterministic and stochastic systems, with an...
Oct 6, 2021 · Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly...
Oct 1, 2021 · Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution tra...
Table 1: Differences between Contraction Theory and Lyapunov Theory. Contraction theory (which constructs positive defi- nite matrix M(x,t) that defines contraction metric)
Mar 1, 2014 · In this work, we present the fundamental results of contraction theory in an intrinsic, coordinate-free setting, with the presentation highlighting the underlying geometric foundation of contraction theory and the resulting stability properties.
This section derives the basic convergence principle of this paper, which we first introduced in (Lohmiller and Slotine, 1996, 1997). Considering the local flow at a given point x leads to a convergence analysis between two neighboring trajectories.
Contraction theory is a more recent tool for ana-lyzing the convergence behavior of nonlinear systems in state-space form; see Lohmiller and Slotine (1998), Slotine and Wang (2003) and Jou roy (2003b) for the explicit incorporation of inputs in the framework of contraction.
Abstract—Contraction theory provides an elegant way to an-alyze the behaviors of certain nonlinear dynamical systems. Under sometimes easy to check hypotheses, systems can be shown to have the incremental stability property that trajecto-ries converge to each other.
Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution tra...
