A stability result with application to nonlinear regulation: theory and experiments

In the present work we consider the control of a class of nonlinear systems described in a pseudo-linear form. The pseudo-linear representation of the system is described and a stability analysis is performed which leads to sufficiency conditions under which local and global asymptotic stability is present. These results are then applied to study stability and convergence properties of closed loop systems which arise when the state dependent Riccati equation (SDRE) technique is used. It is shown that the SDRE technique yields globally asymptotically stabilizing controls for a class of nonlinear systems satisfying certain growth conditions. Additionally, many of the benefits of linear optimal control, such as a tradeoff between state regulation and input effort, are readily transparent in the nonlinear scheme. The application example is a nonlinear benchmark problem first proposed by Kokotovic (1991). A real time experimental controller is applied to the simulated dynamics to demonstrate practical feasibility of the SDRE technique