Input and output coupled nonlinear systems

• Published in: IEEE transactions on circuits and systems. 1, Fundamental theory and applications Fundamental theory and applications, 2005-03, Vol.52 (3), p.567-575
• Main Authors: Duan, Zhisheng, Wang, Jin-Zhi, Huang, Lin
• Format: Article
• Language: English
• Subjects: Chaos; Circuit analysis; Circuits; Control theory; Convergence; Coupled Chua's circuit; Coupling circuits; Design methodology; Dynamical systems; global convergence; input and output interconnection; input transformation; Integrated circuit interconnections; Interconnected systems; Interconnections; Joining; Limit-cycles; Linear matrix inequalities; Nonlinear dynamics; Nonlinear systems; nonlinear systems with multiple equilibria; Nonlinearity; Transformations
• ISSN: 1549-8328; 1057-7122; 1558-0806
• DOI: 10.1109/TCSI.2004.842873

In this paper, a class of input and output coupled nonlinear systems with multiple equilibria are studied. These kinds of systems can also be viewed as interconnected systems composed of single-input and single-output systems through some linear and nonlinear interconnections. Frequency-domain conditions are established for global convergence and convergence of bounded solutions for such systems. The effects of nonlinear input and output interconnections can be studied through a nonsingular matrix. The design method based on linear matrix inequality for the interconnected matrix is presented. In addition, the relation between input and output coupling here and input transformation in control theory is established. The coupling method is illustrated through a coupled Chua's circuit. The nonexistence of chaotic attractors or limit cycles in the coupled Chua's circuit can be analyzed by convergence of bounded solutions.