Generalized Canonical State Models of Third-Order Piecewise-Linear Dynamical Systems And Their Applications

Abstract

The elementary canonical state models of the third-order autonomous dynamical systems, topologically conjugate to Chua's circuit family, are generalized for any continuous and odd symmetrical piecewise-linear (PWL) feedback function. Their state equations are in accordance with the basic form of the Lur'e systems and the corresponding circuit model contains the multiple PWL feedback. The general results are applied for the simplest three-region case defined by three sets of the equivalent eigenvalue parameters. The application of these results is demonstrated on the double-scroll chaotic attractor with global attracting properties. As an example its utilization in synchronized chaos is shown.