One New Approach for Synthesis of Nonlinear Dynamic Systems Based on State Space Energy Approach

摘要

Most systems today have been developed under the linearity assumption and are carried out using electronic devices that are essentially linear. Thus in many cases inherently nonlinear devices have to be linearized in order to achieve a certain degree of the resulting linear system performance. Another possibility is nonlinear approach. The synthesis of nonlinear dynamic systems is of outstanding importance for numerous engineering applications. The techniques that are proposed in this lecture are based on state space energy approach. Presented study deals with energy, stability and related structural properties of a relatively broad class of finite dimensional strictly causal systems, which can be described in the state-space representation form. Dissipativity, instability, asymptotic stability as well as stability in the sense of Lyapunov is analyzed by a new approach based on an abstract state energy concept. We present also a one new method for synthesizing nonlinear dynamic circuits. One advantage of our approach is that we can directly synthesize nonlinear circuits from some ordinary differential equations. Presented circuit is able to generate the conservative chaotic attractors. This system can be used e.g. for secure communication, modulation etc. On the beginning we start with a simple motivation example of a nonlinear system described by the 3rd - order differential equation. We continue by adding linear parts of different order. Finally, the robust chaos-generating systems of arbitrary finite order with possibility of system order switching are shown. The designed systems were simulated and partly constructed in digital versions. Results of simulation and measuring are also presented.