Nonlinear static and dynamic output feedback controllers for passive systems: global stabilization and local optimality

We extend the H₂-based and mixed-norm H₂/H _∞-based positive real controller synthesis methods developed by Lozano-Leal et al.(1988) and Haddad et al. (1994) to nonlinear passive dynamical systems. Specifically, globally stabilizing static and dynamic output feedback nonlinear controllers are constructed for nonlinear passive systems that additionally minimize a nonlinear-nonquadratic performance criterion involving a nonlinear nonquadratic, nonnegative-definite function of the state and a quadratic positive-definite function of the control. In particular, by choosing the nonlinear-nonquadratic weighting functions in the performance criterion in a specified manner, the resulting static and dynamic controllers are guaranteed to be strictly passive. We show that the linearized controller for the linearized passive system is H₂ optimal. Finally, globally optimal, stabilizing static output feedback controllers for nonlinear passive systems that additionally guarantee a disturbance rejection constraint in the face of L₂ disturbances are also developed