The field of feedback control design for nonlinear systems has been continuously developing in recent decades, because of its practical importance and challenging theoretical nature. Kinetic systems are able to produce all the important qualitative phenomena present in nonlinear systems, so they form a rich-enough sub-class. It is well-known that the utilization of the physical and/or structural specialties of different nonlinear system classes greatly helps in obtaining theoretically well-grounded, powerful and practically still feasible analysis and control methods.
The realization theory of kinetic systems makes a connection between the structural properties and dynamical behaviour (e.g. weak reversibility and deficiency).
The greatest difficulty of the realization based system analysis is that a system may have more than one realization. In this diploma work different optimization based realization computation methods are presented for computing realizations with desired properties. The existed results are summarized and new ones are introduced.
Feedback design methods are proposed for polynomial systems with linear input structure. These methods based on the optimization based realization computation methods. Therefore, the dynamical behaviour of the closed loop can be easily prescribed with optimization constraints. The introduced methods are extended to polynomial system with parametric uncertainty.