Nonlinear controller design based on control Lyapunov functions

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We have proposed an asymptotically stabilizing controller and an adaptive controller for input affine nonlinear systems with convex input constraints by using given control Lyapunov functions. We have designed a global inverse optimal controller with local homogeneity for locally homogeneous input affine nonlinear systems by using locally homogeneous control Lyapunov functions. The proposed controller guarantees the local convergence rates and sector margins. We have clarified that local convergence rates and sector margins are invariant under coordinate transformations. We have proposed a global inverse optimal controller that is LQ optimal in a small neighborhood of the origin.