Nonlinear Control Based on State-dependent Coefficient Systems

The nonlinear affine systems were represented by state-dependent coefficient systems. In a short time interval, the state-dependent coefficient systems could be approximated by linear systems, with which linear stabilizing controllers were designed and used to stabilize the original nonlinear affine systems. The stability of the closed–loop systems was ascertained under the condition that the coefficients matrices were commutative. The design approach can be combined with many design methodologies for linear systems, and has the advantages of simplicity and avoiding the construction of complex Lyapunov functions. Simulation of the cart pendulum system shows the effectiveness of the design method.