Here, a new method for solving the H∞ control problem for a class of affine nonlinear singular systems is presented. The main idea is to restrict the control inputs and initial states to the sets of admissible inputs and consistent initial values, respectively. Consequently, the impulse-freeness of the system response is guaranteed. In this regard, a novel concept of “distance from the admissible inputs set” is introduced. Based on this concept, a set of sufficient conditions for the H∞ control problem's solvability and the corresponding H∞ controller is provided. The adopted approach can also be employed to solve the H∞ control problem for indefinite nonlinear singular systems as well as non-singular nonlinear systems with a restricted inputs set. Sufficient conditions for the solvability of and corresponding solution to these problems are also presented. Finally, the practicality of this method is illustrated using a numerical example.
Shojaee, V., Shafiee, M., & Ibeas, A. (2022). State feedback H∞ control for a class of affine nonlinear singular systems: Input restricting approach. IET Control Theory and Applications, 16(2), 166–181. https://doi.org/10.1049/cth2.12213