Our paper is devoted to studying and designing novel chaotic systems based on known coordinate transformations from one coordinate system into another. As the initial data for such transformation, we take into account a discrete-time model for the generalized dynamical system and show its usage to solve direct and inverse dynamic problems. We consider the solution of the first one to be an equation of a system transmitter, and the last one defines the motion of the receiver subsystem. The above-mentioned transformation is based on the coordinate transformation from a Cartesian coordinate system into an angular one. The use of matrix methods allows us to define highly formalized generalized expressions that perform the above-mentioned direct and inverse coordinate transformations. These expressions and system equations can be considered state space finite difference-algebraic equations. In his case, the transformation equations can be considered as equations of some nonlinear observer. One can rewrite these equations in the finite-difference form to simplify the system analysis by substituting the observer equations into initial system ones. Our studies in solving inverse dynamic problem define several ways that one can consider as backgrounds to establish secured communication schemes. We show the use of our approach by considering the transformation of the well-known Chua circuit dynamic from Cartesian to angular coordinates and vice versa. The studies of these transformations’ results prove the possibility of designing novel chaotic systems.