Non-weighted H∞ performance for 2-D FMLSS switched system with maximum and minimum dwell time

• Published in: Journal of the Franklin Institute Vol. 356; no. 11; pp. 5729 - 5753
• Main Authors: Hua, Dingli, Wang, Weiqun, Yao, Juan, Ren, Yuanhong
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.07.2019; Elsevier Science Ltd
• Subjects: Attenuation; Dwell time; H infinity; Liapunov functions; Mathematical functions; Mathematical models; Numerical analysis; Subsystems; Switching; Two dimensional models
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2019.05.025

This paper investigates the H∞ performance of two-dimensional (2-D) switched system represented by Fornasini–Marchesini local state-space (FMLSS) model with maximum and minimum dwell time approach. By using the multiple Lyapunov function approach, and designing a set of switching signals subject to maximum and minimum dwell time characteristic, respectively, for all stable subsystems or both stable and unstable subsystems exist, we give the sufficient condition on exponential stability of the given switched system, and propose the sufficient condition which can guarantee that the given switched system is exponentially stable and has a specified H∞ disturbance attenuation level γ. All the results obtained are on normal noise attenuation index of strictly non-weighted form, which are better than the existing results on weak one of weighted form from the physical point of view. Finally, numerical examples are presented to display the effectiveness of the proposed results.