# Fractional and multidimensional systems work-group

The dilemma for the control engineer has always been to find the proper model, close enough to the real system but simple enough to allow its study and its use. With the development of numerical algorithms and powerful computers, new models have been proposed in order to reflect more accurately the real systems. Among these new models, one can find the so called *fractional systems *(where the derivatives representing the system are not necessarily integers) and *multidimensional systems *also known as *nD systems* (where the equations take into account the fact that the information doesn’t necessarily propagate in only one direction, a usual simplification). The members of this group are therefore interested in the identification, analysis and control of such systems. The theoretical problems are however so wide that a focus on a few particular techniques has been chosen.

Therefore, the main issues presently considered are:

- Identification and analysis (stability) of nD and fractional systems;
- Control of systems with delays via nD models;
- Analysis and control of nD and fractional systems using robust control approaches;
- Modelling and identification of processes governed by Partial Differential Equation (PDE) (diffusion, propagation) using fractional and nD systems.

The main application fields presently considered are:

- Thermal systems characterization;
- Electrochemical systems characterization (batteries, ultracapacitors);
- Heat exchangers;
- Hot springs (geothermal energy).