$$H_\infty $$H∞ Control and $$\varepsilon $$ε-Bound Estimation of Discrete-Time Singularly Perturbed Systems

This paper considers the problems of $$H_\infty $$H∞ control and $$\varepsilon $$ε-bound estimation of discrete-time singularly perturbed systems. A set of well-defined conditions for the existence of state feedback controllers are proposed, under which the resulting closed-loop system is asymptotically stable while satisfying a prescribed $$H_\infty $$H∞ norm bound when the singular perturbation parameter $$\varepsilon $$ε is lower than a pre-defined upper bound. It is shown that the proposed controller design method is less conservative than the existing ones. Furthermore, a method of estimating the $$\varepsilon $$ε-bound is proposed, which leads to less conservative results and requires lower computational burden than the existing methods for a wide class of singularly perturbed systems. Finally, examples are given to show the advantages and effectiveness of the obtained results.