カスケード系のほぼ大域的漸近安定性を証明する合成的手法
A Compositional Approach to Certifying the Almost Global Asymptotic Stability of Cascade Systems
サブシステムがほぼ大域的漸近安定なカスケード系について、有界な前方軌道と成長率条件から全体のほぼ大域的漸近安定性を保証する十分条件を与え、上三角系に拡張した。
著者: Jake Welde, Matthew D. Kvalheim, Vijay Kumar
分類: math.OC, cs.RO, math.DS
原文アブストラクト
In this work, we give sufficient conditions for the almost global asymptotic stability of a cascade in which the subsystems are only almost globally asymptotically stable. The result is extended to upper triangular systems of arbitrary size. In particular, if the unforced subsystems are almost globally asymptotically stable and their only chain recurrent points are hyperbolic equilibria, then the boundedness of forward trajectories is sufficient for the almost global asymptotic stability of the full upper triangular system. We show that unboundedness of such cascades is prohibited by growth rate conditions on the interconnection term and a Lyapunov function for the unforced outer subsystem, and the required structure for the chain recurrent set is enjoyed by classes of systems common in geometric control e.g. dissipative mechanical systems. Our results stand in contrast to prior works that require either time scale separation, prohibitively strong disturbance robustness properties, or global asymptotic stability in the subsystems.
