Abstract
This paper focuses on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H\infty $ </tex-math></inline-formula> observer-based control problem for discrete-time singularly perturbed systems (DTSPSs) with nonlinear disturbances. The main contributions of this paper include three aspects: First, a proper observer is constructed. A sufficient condition in terms of linear matrix inequality (LMI) and Lyapunov function is proposed such that the resulting observer error system is asymptotically stable with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> norm bound for sufficiently small values of the perturbation parameter. Second, based on the input-to-state stability (ISS) property, an observer-based feedback controller is designed such that the resulting closed-loop system is ISS with respect to the observer error. Meanwhile, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H\infty $ </tex-math></inline-formula> performance index is also satisfied. Then, a workable way for solving the exact upper bound is also given. Finally, two numerical examples are given to demonstrate the validity of the developed method.
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