Passivity Of Switched Nonlinear Systems And Its Applications To Network Synchronization

Switched nonlinear systems, as a special but important class of hybrid systems, are of great significance in acedamic study. Also, such systems have wide applications in engineering practice. However, the hybrid characteristic of switched systems and the inherent complexity of nonlinear systems make the theoretical study and applications of switched nonlinear systems much difficult. No systematical results of the study on such systems have been available so far. On the other hand, passivity, as an important system property, has been widely applied in the analysis and design of non-switched systems and a systematical theory has been formed. For switched systems, the study on passivity is just at the early stage, many problems are far from being understood and thus deserve investigation.This dissertation mainly studies on passivity of switched nonlinear systems, and extends the passivity-based control theory to the study of output synchronization of dynamical networks. Both the classical passivity and generalized passivity of switched systems are investigated. Generalized passivity is defined for switched systems for the first time. Furthermore, output quasi-passivity is presented to study the proposed generalized output synchronization of dynamical networks. The main methods used in this dissertation include the multiple storage function method, the multiple Lyapunov function method, the average dwell time approach and the convex combination technique.The main contributions of this dissertation are as follows.1. Passivity and feedback passivation of switched nonlinear systems are investigated using multiple storage functions. The concept of storage-like functions for switched systems is presented. A sufficient condition for passivity of switched nonlinear systems is given via multiple storage functions under some switching signal. Then, the result is extended to find conditions under which a switched system is feedback equivalent to a passive switched system. Furthermore, passivity of switched cascade systems is investigated.2. The issues of generalized passivity, feedback equivalence and stability for switched nonlinear systems via a multiple storage function method are addressed. Since the storage function of each subsystem may jump at the "switched on" time sequences, the classic passivity may not be satisfied for switched systems. A concept of generalized passivity for switched systems is presented by multiple storage-like functions. Based on this, the conditions for generalized passivity of switched nonlinear systems are given. Furthermore, the problem of feedback passivation and the passivity-based stability of switched nonlinear systems are investigated.3. The stabilization issue for switched nonlinear systems with passive and non-passive subsystems is investigated. For any given average dwell time, if the total activation time rate of passive subsystems in any time interval is larger than any given constant, no matter how small it is, feedback controllers can be designed with respect to the average dwell time and the activation time rate of passive subsystems to achieve exponential stabilization.4. The generalized output synchronization problem for dynamical networks using the output quasi-passivity property of each node is addressed. The generalized output synchronization manifold is defined to characterize generalized output synchronization. Using output quasi-passivity, which is defined as a special type of dissipativity and as a generalization of output strict passivity, some criteria for generalized output synchronization are given without assuming the negative definiteness property of the coupling matrix of the network. Furthermore, when a single coupling topology cannot guarantee generalized output synchronization by output quasi-passivity, an appropriate switching between several coupling topologies can achieve generalized output synchronization.5. The output synchronization problem of dynamical networks consisting of nodes with relative degree one is studied. Passivity is usually a useful tool to output synchronize a dynamical network. It is well known that if a nonlinear system is weakly minimum phase and has relative degree one, then it is feedback equivalent to a passive system. The feedback passivation result is exploited to investigate output synchronization of dynamical networks. The conditions, under which output synchronization of dynamical networks with relative degree one is achieved, are given, and the negative definiteness property of the outer coupling matrix is not assumed. Furthermore, when each node is feedback equivalent to an output strictly passive system, the output synchronization criterion is presented with less conservative conditions. Finally, several coupling topologies are exploited to achieve output synchronization of dynamical networks by the use of feedback passivation theory and switching.The conclusions and perspectives end the dissertation.