Consider a C vector field together with an ergodic invariant probability that has l nonzero Lyapunov exponents. Using orthonormal moving frames along certain transitive orbits we construct a linear system of l differential equations which is a reduced form of Liao’s “standard system”. We show that the Lyapunov exponents of this linear system coincide with all the nonzero exponents of the given ...

The non-autonomous bouncing ball system consists of a point mass m in a constant gravitational field g, which bounces inelastically on a flat vibrating table. The presented Lyapunov-like method is set up for non-autonomous measure differential inclusions and constructs a decreasing step function W above the oscillating Lyapunov function V . Furthermore, it is proven that the attractivity of the...

†A *C We give Lyapunov-like conditions for non-uniform in time output stabilization of discrete-time systems. Particularly, it is proved that for a discrete-time control system there exists a (continuous) output stabilizing feedback if and only if there exists a (strong) output control Lyapunov function (OCLF). Moreover, strategies for the construction of continuous robust feedback stabilizers ...

This work provides a generalization of a converse Lyapunov theorem for systems that do not have the regularity property on the invariant sets. As an application , we provide Lyapunov-function like necessary and suucient characterizations for the problem of ISS-disturbance attenuation.

In this paper, we introduce some analysis tools for switched and hybrid systems. We first present work on stability analysis. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems (IFS) theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set. Finally, we e...

Swarm principles are increasingly being used to design controllers for the coordination of multi-robot systems or, in general, multi-agent systems. This paper proposes a two-dimensional Lagrangian swarm model that enables the planar agents, modeled as point masses, to swarm whilst effectively avoiding each other and obstacles in the environment. A novel method, based on an extended Lyapunov app...