Open AccessState feedback H ∞ control for a class of affine nonlinear singular systems: Input restricting approach
Author(s) -
Shojaee Vahid,
Shafiee Masoud,
Ibeas Asier
Publication year - 2022
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/cth2.12213
Subject(s) - nonlinear system , control theory (sociology) , mathematics , affine transformation , impulse (physics) , class (philosophy) , state (computer science) , set (abstract data type) , singular solution , controller (irrigation) , singular control , control (management) , optimal control , mathematical optimization , computer science , mathematical analysis , algorithm , pure mathematics , artificial intelligence , physics , quantum mechanics , agronomy , biology , programming language
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.