Design of stabilizing controllers for nonlinear systems

This paper is focused on developing a new approach to nonlinear control synthesis using tangent linearization control and state-dependent Riccati differential equations. Motivated by recent results on tangent linearization control, the nonlinear feedback stabilization problem for nonlinear systems is firstly reduced to that of a feedback stabilizing controller design for linear time-varying systems. And 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 needs 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.