Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators

We study the robustness of optimal regulators for nonlinear, deterministic and stochastic multiinput dynamical systems, under the assumption that all state variables can be measured. We show that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.