Review on contraction analysis and computation of contraction metrics

Contraction analysis considers the distance between two adjacent trajectories. If this is contracting, then trajectories have same long-term behavior. The main advantage of that it independent solutions under consideration. Using an appropriate metric, with respect to which one can show convergence a unique equilibrium or, if attraction only occurs in certain directions, periodic orbit.Contraction was originally considered for ordinary differential equations, but has been extended discrete-time systems, control delay equations and many other types systems. Moreover, similar techniques be applied estimation dimension attractors different notions entropy (including topological entropy).This review attempts link references both mathematical engineering literature and, furthermore, point out recent developments algorithms computation contraction metrics.