Dissipativity analysis and stabilization for discontinuous delayed complex-valued networks via matrix measure method

Abstract

Abstract In this paper, we discuss the dissipativity and stabilization problems via matrix measure strategy. First, we propose a way to construct complex-valued set-valued maps and give the basic framework of complex-valued differential inclusions. In addition, based on matrix measure strategy and the generalized Halanay inequality, we analyze the dissipativity of the addressed discontinuous complex-valued neural networks by using two different ways. Furthermore, we design a set of controllers to guarantee the exponential stability of the studied networks. The main contribution of this paper is an extension of the dissipativity results of traditional neural networks to discontinuous ones. Finally, we give numerical examples to substantiate the merits of the obtained results.

Keywords

• Complex-valued networks
• Dissipativity analysis
• Differential inclusion
• Matrix measure method
• Generalized Halanay inequality