Abstract
Generalized synchronization (GS) in nonlinear systems appears when the states of one system, through a functional mapping are equal to states of another. This mapping can be obtained if there exists a differential primitive element which generates a differential transcendence basis. We introduce a new definition of GS in nonlinear systems using the concept of differential primitive element. In this contribution, we investigate the GS problem when we have strictly different nonlinear systems and we consider that for both the slave and master systems only some states are available from measurements. The first component of the mapping is called differential primitive element and, in general, is defined by means of a linear combination of the known states and the inputs of the system. Furthermore, we design a new dynamical feedback controller able to achieve complete synchronization in the coordinate transformation systems and GS in the original coordinates. These particular forms of GS are illustrated with numerical results of well-known chaotic benchmark systems.
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