A new approach to controller synthess for nonlinear systems

A new approach to nonlinear controller synthesis is proposed using tangent linearization control and state-dependent Riccati differential equation. Motivated by tangent linearization control, the nonlinear feedback stabilization problem for nonlinear systems is first reduced to that of a feedback stabilizing controller design for linear time-varying state-dependent systems. Then, a state-dependent Riccati differential equation based approach is presented to design of state-feedback controller of the deduced linear time-varying system. To implement such a controller, only a state-dependent Riccati differential equation with given positive definite initial condition need to be solved online. Moreover, it is shown analytically that the closed-loop system under the proposed nonlinear feedback is exponentially asymptotically stable. Finally, a numerical example shows the effectiveness of the proposed approach.