Stability of dynamical polysystems via families of Liapunov functions

Liapunov’s direct method for Birkhoffian systems: Applications to electrical networks

In this paper, the concepts and the direct theorems of stability in the sense of Liapunov, within the framework of Birkhoffian dynamical systems on manifolds, are considered. The Liapunov-type functions are constructed for linear and nonlinear LC and RLC electrical networks, to prove stability under certain conditions.

Dynamics of a discrete-time plant-herbivore model

An Equivariant Liapunov Stability Test and the Energy–momentum–casimir Method

We present an equivariant Liapunov stability criterion for dynamical systems with symmetry. This result yields a simple proof of the energy–momentum–Casimir stability analysis of relative equilibria of equivariant Hamiltonian systems.

Stability analysis of predator-prey models via the Liapunov method.

As is well known from the classical applications in the electrical and mechanical sciences, energy is a suitable Liapunov function; thus, by analogy, all energy functions proposed in ecology are potential Liapunov functions. In this paper, a generalized Lotka-Volterra model is considered and the stability properties of its non-trivial equilibrium are studied by means of an energy function first...

Ela Multi - Agent Avoidance Control Using an M - Matrix Property ∗

In this paper a generalization of avoidance control for multi-agent dynamic systems is presented. Strategies for avoidance control for multiple agents are obtained using individual Liapunov-type functions. The overall system avoidance conditions are guaranteed using a vector Liapunov-type function via an M-matrix property.