Control of chua's circuit with a cubic nonlinearity via nonlinear linearization technique

This paper addresses the controlling chaos problem of a cubic variant for the original Chua's circuit. A conventional input-output transfer function of a linearized system and a nonlinear linearization technique for a nonlinear system are also presented. According to analytical results, at equilibrium, the notion of local phase-minimality of the nonlinear system is equivalent to that of the linear system's transfer function. Our results also demonstrate that the controlled Chua's circuit, while considering a certain state as the system output, is an input-output linearizable minimum-phase system. In addition, nonlinear control laws are derived such that each state asymptotically tracks its corresponding desired trajectory while maintaining the boundedness of all signals inside the system.