Design of a Robust H∞ Controller for Affine Nonlinear Singular Systems with Norm-bounded Time-varying Uncertainties

In this paper, the problem of robust H∞ control for continuoustime affine nonlinear singular systems with normbounded timevarying uncertainties is addressed. The problem is solved locally by employing two different approaches. The first approach is an extended version of the guaranteed cost control method, adapted in order to conform to affine nonlinear singular systems. The second approach is an indirect method in which a known auxiliary system is presented and it is shown that any control law which solves the H∞ control problem for this auxiliary system, also solves the robust H∞ control problem for the original unknown system. In both approaches, sufficient conditions for the solvability of the considered robust H∞ control problem are provided in terms of a generalized HamiltonJacobiIsaacs inequality. In order to show the consistency of our results, solving the robust H∞ control problem for linear uncertain singular systems is considered, and, it is shown that the corresponding results in linear domain are the special cases of our results. Finally, a numerical example is given to illustrate the applicability of the presented approaches.