Controller design based on similar skew-symmetric structures

Backstepping controller design is simplified and extended to more applications by proving the asymptotic stability of a class of nonlinear system chosen as the controller design goal. Design procedures are developed using backstepping and direct construction. Backstepping is applicable to general plants with a lower triangular structure, allowing more design parameters than existing methods. The Lyapunov function does not need to be constructed or the construction is only required for partial subsystems; hence, the design is simplified. For some plants with a special lower triangular structure, direct construction can further simplify both the structure and the controller design process. Direct constructure can also be applied to some nonlinear plants for which backsteppping is not feasible.