In this paper, we address the robust filtering problem for a wide class of systems whose state-space data assume a very general nonlinear dependence in the uncertain parameters. Our resolution methods rely on new linear matrix inequality characterizations of 2 and performances, which, in conjunction with suitable linearization transformations of the variables, give rise to practical and computa...

The dissipative soliton regime is one of the most advanced ways to generate high-energy femtosecond pulses in mode-locked lasers. On the other hand, the stimulated Raman scattering in a fibre laser may convert the excess energy out of the coherent dissipative soliton to a noisy Raman pulse, thus limiting its energy. Here we demonstrate that intracavity feedback provided by re-injection of a Ram...

Two one-sided conservation form difference approximations to a scalar one-dimensional convex conservation law are introduced. These are respectively of first- and second-order accuracy and each has the minimum possible band-width. They are nonlinearly stable, they converge only to solutions satisfying the entropy condition, and they have sharp monotone profiles. No such stable approximation of ...

A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (“acceleration equal force”) equations of motion, featuring one-body (“external”) and pair (“interparticle”) forces. The former depend quadratically on the velocity, and nonlinearly on the coordinate, of the moving particle. The latter depend linearly on the coordinate of the moving parti...

A large class of problems in parameter estimation concerns nonlinearly parametrized systems. Over the past few years, a stability framework for estimation and control of such systems has been established. We address the issue of parameter convergence in such systems in this paper. Systems with both convex/concave and general parameterizations are considered. In the former case, sufficient condi...

We study the effect of nonlinearity on systems with periodic parity-time (PT) symmetry, and show that nonlinearity can transform the system from broken to full PT symmetry and vice versa. Furthermore, we show that even when the nonlinearity is insufficient to induce a transition from broken to full PT symmetry, still, the wave functions neither decay nor diverge, despite the fact that the syste...