We consider actions of Z, k ≥ 2, by Anosov diffeomorphisms which are uniformly quasiconformal on each coarse Lyapunov distribution. These actions generalize Cartan actions for which coarse Lyapunov distributions are onedimensional. We show that, under certain non-resonance assumptions on the Lyapunov exponents, a finite cover of such an action is smoothly conjugate to an action by toral automor...

For both discrete-time and continuous-time linear multi-variable control systems, we introduce a concept of control Lyapunov modes associated with a control Lyapunov function in a quadratic form. We prove that the number of unstable control Lyapunov modes is at most equal to the number of input of the system.

As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function. To separate out these two directions and to apply Lyapunov analysis effectively in directions for which Lyapunov exponents are not...

We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schrödinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose Lyapunov exponent is discontinuous, are dense in the space of limit-periodic potentials.

Lyapunov drift and Lyapunov optimization are powerful techniques for optimizing time averages in stochastic queueing networks subject to stability. However, there are various definitions of queue stability in the literature, and the most convenient Lyapunov drift conditions often provide stability and performance bounds only in terms of a time average expectation, rather than a pure time averag...

In linear stability analysis of a large-scale dynamical system, we need to compute the rightmost eigenvalue(s) for a series of large generalized eigenvalue problems. Existing iterative eigenvalue solvers are not robust when no estimate of the rightmost eigenvalue(s) is available. In this study, we show that such an estimate can be obtained from Lyapunov inverse iteration applied to a special ei...

Lyapunov functions for general systems are difficult to construct. However, for autonomous linear systems with exponentially stable equilibrium, there is a classical way to construct a global Lyapunov function by solving a matrix equation. Consequently, the same function is a local Lyapunov function for a nonlinear system. In this paper, we generalise these results to time-periodic and, in part...

This paper introduces a novel Lyapunov-based adaptive control strategy for spacecraft maneuvers using atmospheric differential drag. The control forces required for rendezvous maneuvers at low Earth orbits can be generated by varying the aerodynamic drag affecting each spacecraft. This can be accomplished, for example, by rotating dedicated sets of drag panels. Thus, the relative spacecraft mot...

This paper studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis methods tha...

Motivated by their important role in smooth dynamical systems, Lyapunov exponents have been conceived decades ago as a means to study the stability of cellular automata (CAs). More precisely, they quantify their sensitive dependence on initial conditions. As a next step towards the establishment of a dynamical systems theory of CAs that is inspired by its analogue for smooth dynamical systems, ...