Diffusive representation for pseudo-differentially damped nonlinear systems

A large class of visco-elastic and elasto-plastic systems, frequently encountered in physics, are based on causal pseudo-differential operators, which are hereditary: the whole past of the state is involved in the dynamic expression of the system evolution. This generally induces major technical difficulties. We consider a specific class of pseudo-differential damping operators, associated to the so-called diffusive representation which enables to built augmented state-space realizations without heredity. Dissipativity property is expressed in a straightforward and precise way. Thanks to state-space realizations, standard analysis and approximation methods as well as control-theory concepts may therefore be used.