Robust H_∞ controller design for uncertain 2D continuous systems with interval time-varying delays

Abstract

The design of delay-dependent robust H∞ controllers is solved here for a class of uncertain 2-D continuous systems: those with interval time-varying delays and norm-bounded parameter uncertainties. By constructing a novel augmented Lyapunov-Krasovskii functional and then using the Wirtinger inequality, a new delay-dependent stability condition is developed, that uses the known lower and upper bounds of the time-varying delays to develop less conservative solutions that previous results in the literature. This condition is then applied to H∞ performance analysis and robust H∞ controller design, using linear matrix inequalities (LMIs).Two numerical examples are presented that illustrate the effectiveness of the proposed method.

Preview control of polytopic time‐varying systems subject to actuator saturation

“…Furthermore, .Lemma [20]. Considering diagonal positive definite matrices , matrices and , a vector‐valued function , we have the following expression: then .Lemma [36]. Given matrices , , and with appropriate dimensions, and is symmetric positive definite, the following inequality holds true: …”

“…Lemma [36]. Given matrices X, Y , and Z with appropriate dimensions, and Y is symmetric positive definite, the following inequality holds true:…”

Admissibility and robust H∞ controller design for uncertain 2D singular discrete systems with interval time‐varying delays

“…The phenomena of time delays are considered here, as they are frequently encountered in many control systems such as communication, process control systems, switched control systems and networked control systems. Many researches shall therefore consider systems with delays for 1D systems (see, e.g., Zhou Gu et al; 18,19 Rajchakit; 20,21 Phat and Ratchagit; 22 Xu and Lam 23 ) and also for 2-D systems (see, e.g., Badie et al; 24,25 Xuhui et al; 26 Dami et al; 27 Van Hien and Trinh; 28 Benhayoun et al; 29 Huang and Xiang 30 ). There have been a few papers concerning the problems of stability and stabilization of 2-D singular systems, for example Zou and Campbell 31 proposed the concept of jump modes and related stability for 2-D singular systems, it must be mentioned that the presence of jump modes can reduce the cost performance index of the system, in fact we must make sure that the previous system is admissible, which means that the system is regular, jump mode free and stable.…”

$$H_{\infty }$$ Model Reduction for 2-D Discrete Markovian Jump Systems

“…As is all known, many modern engineering fields, such as process control, transmission lines, image processing and signal filtering Du and Xie (2002), Kaczorek (1985), Lu (1992), have intrinsic 2-D characteristics, which motivates researchers to study the analysis and the design methods for 2-D systems. Accordingly, many problems on 2-D systems have been addressed; for example, stability and stabilization problems are studied in Badie et al (2018), Badie et al (2019), Tadepalli and Leite (2018), Yao et al (2013), control problem is investigated Badie et al (2020a), Duan and Xiang (2013), Fei et al (2017), Luo et al (2016) and filtering problem is discussed in Badie et al (2020b), Li and Gao (2013), Liang et al (2015), Xu et al (2017).…”