Explicit Construction of H Control Law for a Class of Nonminimum Phase Nonlinear Systems

We tackle in this paper an H_infin control problem for a class of nonminimum phase nonlinear systems. The system nonlinearities, which depend on the system output, can be unknown, but satisfy some linear growth conditions. The given system is first transformed into a special coordinate basis, in which the system zero dynamics is divided into a stable part and an unstable part. A sufficient solvability condition is then established for solving the nonlinear H_infin control problem. Moreover, based on the sufficient solvability condition, an upper bound of the best achievable L₂ gain from the system disturbance to the system controlled output is estimated for the nonlinear H_infin control problem. The proof of our result yield explicit algorithms for constructing required control law for solving the nonlinear H_infin control problem. In particular, the solution to the nonlinear H_infin control problem does not require solving any Hamilton-Jacobi equations. Finally, the obtained results are utilized to solve a benchmark problem on a rotational/translational actuator (RTAC) system.