Dissipative Control of 2-D Switched Discrete System Via Dwell-Time-Dependent Approach
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Dissipative Control of 2-D Switched Discrete System Via Dwell-Time-Dependent Approach Dingli Hua1 · Weiqun Wang1
· Weiren Yu2 · Juan Yao3
Received: 20 October 2019 / Revised: 24 April 2020 / Accepted: 27 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper studies the dissipative control problem for two-dimensional (2-D) switched discrete-time linear system represented by Fornasini–Marchesini local state-space (FMLSS) model via dwell-time-dependent Lyapunov function (DTDLF) approach. Consider the definition of (Q, S, R)-α-dissipativity for 2-D switched discrete FMLSS model in triangular region and based on the DTDLF approach, we first give the linear matrix inequality (LMI)-based sufficient condition on asymptotic stability for the 2-D switched discrete FMLSS model and then propose the LMI-based sufficient condition which can guarantee the given 2-D switched system to be asymptotically stable and strictly (Q, S, R)-α-dissipative. Furthermore, the dwell-time-dependent dissipative state-feedback controller is designed, and the LMI-based sufficient condition for designing such controller is proposed. Besides, dwell-time-dependent passive statefeedback controller and dwell-time-dependent H∞ state-feedback controller could be derived as the special cases of dissipative control from the established result. Finally, illustrative examples are depicted to verify the efficiency and superiority of the proposed techniques. Keywords Dwell-time dependent · 2-D switched systems · Dissipativity · Lyapunov function
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Weiqun Wang [email protected] Dingli Hua [email protected] Weiren Yu [email protected] Juan Yao [email protected]
1
School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
2
Department of Computer Science, University of Warwick, Coventry CV4 7AL, UK
3
School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
Circuits, Systems, and Signal Processing
1 Introduction In the last century, two-dimensional (2-D) systems, whose information propagates along two different directions, have witnessed growing interests in many real-life applications, such as water stream heating, graph data processing, thermal processes, and signal filtering [21]. Generally, 2-D systems can be modeled in various ways. Typical examples include Fornasini–Marchesini local state-space (FMLSS) model [12] and Roesser model [25]. There are many interesting studies on 2-D systems (please refer to, e.g., [1,5,6,14,19,28,30,31,38,39] and the references therein). The related studies on dissipativity for 2-D systems were [1,19,28,30]. Ahn et al. [1] and Wang et al. [30] solved the problems of dissipative control for 2-D Roesser model and FMLSS model by providing sufficient conditions to check asymptotic stability and 2-D (Q, S, R)-α-dissipativity, respectively. Recently, switched systems also have obtained significant attention in the research area of control systems. They can be effectively employed to represent a variety of
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