This paper studies the nonlinear stability of capillary-gravity waves propagating along interface dividing two immiscible fluid layers finite depth. The motion in both regions is governed by incompressible and irrotational Euler equations, with density each being constant but distinct. A diverse collection small-amplitude solitary wave solutions for this system have been constructed several aut...

This paper presents certain generalisations to the classical concepts of wellposedness and internal stability. Input consistency and output uniqueness of the closed-loop system in the standard control feedback configurations are discussed. Based on this, a number of notions are introduced such as fully internal wellposedness, externally internal wellposedness, and externally internal stability,...

In the current study of robust stability of infinite-dimensional systems, internal exponential stability is not necessarily guaranteed. This paper introduces a new class of impulse responses called R, in which the usual notion of L2-input/output stability guarantees not only external but also internal exponential stability. The result is applied to derive a closed-loop stability condition, and ...

This paper studies the nonlinear vibration analysis of a simply supported Euler-Bernoulli beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes concept in the case of three-to-one (3:1) internal resonance. The beam’s governing nonlinear PDE of motion and also its boundary conditions are derived and then solved using the method of Multiple Time ...

In this paper, a new virtual leader following consensus protocol is introduced to perform the internal and string stability analysis of longitudinal platoon of vehicles under generic network topology. In all previous studies on multi-agent systems with generic network topology, the control parameters are strictly dependent on eigenvalues of network matrices (adjacency or Laplacian). Since some ...