Some Topics On Switched Systems And Its Applicaions

Switched systems as an important class of hybrid systems consist of a family of subsystems and a switching rule which orchestrates the switching between them. Switched systems have been widely used in various control engineering, such as power electronics, power systems, chemical processes, network communication, mechanical systems etc.. Meanwhile, switched systems have been used in the study of complex switched networks and multi-agent systems with switching topology. Hence, switched systems have been received more and more attention. However, there are some basic problems about switched systems which have not been solved, e.g. the controllability of switched systems with bound control, the functional relationship between L2gain and dwell time. Hence, This thesis is concerned with these basic problems of switched systems, and the application of switched systems to the synchronization of complex networks and the consensus of multi-agent systems. In the following, the contributions of this thesis will be presented in details.First, this thesis investigates the controllability of a class of switched systems in which the zero control is an extreme point of the control constraint set. This thesis first studies the push-pull systems with control constraint set, and obtains the sufficient and necessary conditions for local controllability at the origin of this class of system. Based on the controllability of push-pull systems, sufficient and necessary conditions are obtained for local controllability at the origin of such switched systems. In addition, sufficient conditions are obtained for local controllability at a nonzero state of such switched systems. Finally, the obtained results are used to study the controllability of Kinetic Battery Model.Second, this thesis investigates L2-induced gain from the input disturbance to output of discrete-time switched linear systems subject to actuator saturation. With the state feedback gains adopted beforehand, the LMI (linear matrix inequalities) formulation is established to estimate the approximate relationship between L2-induced gain and dwell time. Then thsis thesis investigates the influence of parameter variations on the L2-induced gain, and presents a state feedback design method for a fixed dwell time and an upper bound of restricted L2-induced gain. In addition, this thesis investigates the qualitative relationship between disturbances rejection capability and dwell time.Third, this thesis studies the synchronization of complex switched networks with different inner coupling matrices. By using contraction theory, a synchronization criterion is established by the contractivity of lower-dimensional dynamic systems under some conditions on coupling matrices. Compared with the existing literature on synchronization of complex switched networks, the criterion of this thesis has two features. First, the criterion is easy to calculate for synchronization of complex switched networks with different inner coupling matrices. Moreover, this criterion holds for arbitrary switching topology. Second, one can easily use this criterion to obtain a condition for parameters of network to guarantee the synchronization of complex switched network. For a complex switched network with some parameters, one can obtain a inequality about this parameters, which can guarantee the synchronization of complex switched network.Fourth, this thesis studies the consensus problem in second-order multi-agent systems with nonlinear dynamics and switching topology. This thesis assumes that the switching rule is trajectory dependent. In order to obtain a state dependent switching rule such that the second-order multi-agent systems achieve consensus, this multi-agent systems is rewritten as switched nonlinear systems. For the two cases that switching topology is a finite number of undirected graphs and directed graphs, by using Lyapunov-Metzler inequalities, some easily checkable conditions are obtained to guarantee that consensus can be achieved by a state switching rule, respectively.Some numerical examples are presented for every contribution of this thesis. These examples illustrate the effectiveness of the obtained results.