arXiv subjects

Mikhail Krichman

Publications and source records attributed to Mikhail Krichman.

2 recordsLinked to original sources

arXiv2004

Global Stabilization for Systems Evolving on Manifolds

We show that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since we allow discontinuous feedbacks, we interpret the solutions of our systems in the ``sample and hold'' sense introduced by Clarke-Ledyaev-Sontag-Subbotin (CLSS). Our work generalizes the CLSS Theorem which is the special case of our result for systems on Euclidean space. We apply our result to the input-to-state stabilization of systems on manifolds relative to actuator errors, under small observation noise.

math.OC↗

arXiv1999

Input-Output-to-State Stability

This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of ``norm-estimators'', and obtains characterizations of nonlinear detectability in terms of relative stability and of finite-energy estimates.

math.OC↗