Abstract
In this paper, the mixed performance and reachable set of uncertain discrete systems with slow variation interval time-varying delay are considered. The original uncertain discrete systems with interval time-varying delay are first transformed into a switched system. Then, the proposed improved results are used to guarantee the stability and reachable set of the uncertain system with slow variation interval time-varying delay. The mixed performance (H2/H∞) can be derived in the same formulation simultaneously. The design scheme of robust switched control is also developed in this paper. The gains of the controller can be designed and switched to achieve stabilization and mixed performance of the system according to the delay value. Some comparisons with published results are made to show the main contribution of the proposed approach. Finally, some numerical examples are illustrated to show the main results.
Highlights
Time delay is confronted in many practical systems, such as chemical engineering systems, hydraulic systems, inferred grinding models, neural networks, population dynamic models, and rolling mills
The dynamics of switched systems comprise a family of subsystems and use a switching signal to handle the switching between the subsystems
In [6], the reachable set of a discrete system with interval time-varying delay was estimated by the Lyapunov method
Summary
Time delay is confronted in many practical systems, such as chemical engineering systems, hydraulic systems, inferred grinding models, neural networks, population dynamic models, and rolling mills. In [6], the reachable set of a discrete system with interval time-varying delay was estimated by the Lyapunov method. To the best of the authors’ knowledge, there are few results considering the reachable set and mixed performance of an uncertain discrete system with interval time-varying delay and linear fractional perturbations. (1) Reachable set estimation and mixed H2/H performance for an uncertain discrete system with interval time-varying delay and linear fractional perturbations are considered in this paper. Less conservative results for an uncertain discrete system with slow variation interval time-varying delay are provided for more accurate estimation of the reachable set. (3) The LMI optimization approach is used to guarantee the minimization of the reachable set and achievement of mixed performance of the system under consideration.
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