Abstract
In this paper, stabilization is studied for a two-dimensional delta operator system with time-varying delays and actuator saturation. Both lower and upper bounds of the time-varying delays are considered. An estimate of the domain of attraction for the two-dimensional delta operator system is introduced to analyze stability of the closed-loop system. A state feedback controller is designed via a Lyapunov–Krasovskii functional approach for the two-dimensional delta operator system with time-varying delays and actuator saturation. Two numerical examples are given to illustrate the effectiveness and advantages of the developed techniques.
Highlights
A 2-D system is a dynamic process in which information is transmitted in two independent directions. 2-D systems are widely studied due to the fact that many practical systems are usually modeled as the 2-D systems, such as signal and image processing [1], thermal processing [2], metal rolling processing [3], and so on
Example 2 A 2-D delta operator system with time-varying delays and actuator saturation is given as δx(ti+1, tj+1) = A 1x(ti+1, tj) + A 1dx ti+1, tj – d1(tj) + B 1 sat u(ti+1, tj)
5 Conclusion In this paper, the stabilization problem has been shown for the 2-D delta operator system with time-varying delays and actuator saturation
Summary
A 2-D system is a dynamic process in which information is transmitted in two independent directions. 2-D systems are widely studied due to the fact that many practical systems are usually modeled as the 2-D systems, such as signal and image processing [1], thermal processing [2], metal rolling processing [3], and so on. There is a lot of space to extend the 2-D systems with time delays into delta domain, which motivates us to make an effort in this paper. Using a delta operator approach, a fuzzy fault detection filter and a stability problem have been investigated for uncertain fuzzy and networked control systems, respectively [15, 16]. A 2-D system is considered in delta domain to adapt to a fast sampling rate and avoid the system instability caused by the fast sampling in this paper Both time-varying delays and actuator saturation, which usually occur in the modern engineering field, are studied for a 2-D delta operator system. The stabilization problem is shown for the 2-D delta operator system with time-varying delays and actuator saturation in Sect. ∂ x(s,t) ∂t denote partial derivatives of function x(s, t) to variables s and t, respectively
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