Research On Passive Stability Of Several Nonlinear Systems

Complex nonlinear networks, owing to their widespread applications and crossdisciplinary nature, have penetrated into many fields, such as engineering, mathematical subject, life sciences and so on. Nowadays, the research on complex networks has become a very challenging subject. The main research progresses in the study of complex networks are concentrated in: network topology characteristics and model, cascading,search algorithm, and the control and synchronization of complex networks. However, the study of passive stabilization and synchronization is fairly few to our knowledge.Meanwhile, results regard to the passively input-to-state stability are quite less common.This paper mainly focuses on passivity problems related to complex nonlinear networks,and input-to-state stability problems of switched nonlinear systems. The main results are as follows:1. Passive stabilization and passive synchronization of complex nonlinear networks.Two classes of complex linear networks are considered with or without time delays(including the state time-varying delays, feedback time-varying delays and interconnection time-varying delays). The purpose of passive stabilization and passive synchronization is to design a state feedback controller such that the nonlinear dynamical network and the corresponding error dynamical network are to be passive and stable asymptotically. Delay-independent sufficient conditions for complex nonlinear networks without delays and delay-dependent sufficient conditions for complex nonlinear networks with time-varying delays are provided, respectively, to solve the passive stabilization and passive synchronization problems for the given networks. Two numerical examples illustrate the effectiveness of the proposed results.2. Passively input-to-state stability of switched nonlinear systems based on storage functions.A kind of switched nonlinear systems are studied to estimate the passively input-tostate stability. First, some definitions related to passivity, such as passively input-to-state stability, energy attenuation domain and so on, are presented. Second, a criterion estimating the passively input-to-state stability is put forward based on the common storage function approach. Then, based on the multiple storage function approach, a criterion is also proposed to estimate the passively input-to-state stability. At last, one numerical example shows the effectiveness of the proposed results.3. Input-to-state stability of switched nonlinear systems via a mode-dependent average dwell time of fast switching approach.A group of switched nonlinear systems are researched to estimate the input-to-state stability. Firstly, a definition of mode-dependent average dwell time of fast switching is given. Secondly, based on both the common average dwell time method and the modedependent average dwell time of fast switching approach proposed, a sufficient condition is provided to ensure the input-to-state stability. Finally, a numerical example demonstrates the efficiency of the obtained results.