Transformation of CLF to ISS-CLF for Nonlinear Systems with Disturbance and Construction of Nonlinear Robust Controller with L2 Gain Performance

Abstract

A new nonlinear control law for a class of nonlinear systems with disturbance is proposed. A control law is designed by transforming control Lyapunov function (CLF) to input-to-state stability control Lyapunov function (ISS-CLF). The transformed CLF satisfies a Hamilton-Jacobi-Isaacs (HJI) equation. The feedback system by the proposed control law has characteristics of L2 gain. Finally, it is shown by a numerical example that the proposed control law makes a controller by feedback linearization robust against disturbance.