In this short paper we study the problem of existence of a controlled behavior that is strictly dissipative with respect to a quadratic supply rate. The relation between strictness and the rank of a suitable qudratic differential form that couples the dissipativity properties of the hidden behavior and the orthogonal complement of the plant behavior is analyzed.

A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.

Article history: Received 2 April 2016 Received in revised form 21 July 2016 Accepted 26 July 2016 Available online 29 July 2016

Philippe Grelu,* Wonkeun Chang, Adrian Ankiewicz, Jose M. Soto-Crespo, and Nail Akhmediev Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 5209 CNRS, Université de Bourgogne, 9 Avenue A. Savary, BP 47870, Dijon CEDEX 21078, France Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies, The Australian National University, Canberra, Australian Cap...

Many dissipative optical systems support patterns. Dissipative solitons are generally found where a pattern coexists with a stable unpatterned state. We consider such phenomena in driven optical cavities containing a nonlinear medium (cavity solitons) and rather similar phenomena (feedback solitons) where a driven nonlinear optical medium is in front of a single feedback mirror. The history, th...

A horizontal layer containing a miscible mixture of two fluids can produce dissipative solitons when heated from below. The physics of the system is described, and dissipative solitons are computed using numerical continuation for three distinct sets of experimentally realizable parameter values. The stability of the solutions is investigated using direct numerical integration in time and relat...

Noncritical strings in the " coupling constant " phase space and bosonic string in the affine-metric curved space are dissipative systems. But the quantum descriptions of the dissipative systems have well known ambiguities. We suggest some approach to solve the problems of this description. The generalized Poisson algebra for dissipative systems is considered.

The strict-contractivity and the convergence of General Linear Methods on the classes of strictly dissipative and dissipative differential systems regarding some inner product are analyzed. New convergence and contractivity results of the methods on semi-infinite intervals are provided for the case of strictly dissipative problems. Some applications of the main results to the class of Runge-Kut...

We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa–Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from H1(R). In particular, the supersonic solitary shock w...