The effects of state feedback and input transformation with application to Lur'e systems

Given a linear system, necessary and sufficient conditions are established for the existence of a state feedback and input transformation such that the closed-loop system becomes extended strictly positive real (ESPR) or SPR. The application to Lur'e systems is also given. The results show that a multivariable Lur'e system with bounded sector constraints can always be stabilized by a state feedback and input/output coupling under a stabilizability condition. An extended Chua's circuit with two nonlinear functions is given as an example to illustrate the results.