ABSTRACT
In this article, we develop two invariance principles for nonlinear discrete-time switched systems based on multiple Lyapunov functions and multiple weak Lyapunov functions, respectively, which allow the first differences of multiple weak Lyapunov functions to be positive on certain sets. It is shown that the solution of the system is attracted to the largest weakly invariant set in a certain specific region. Then, based on the invariance principle developed and geometrical dissipativity, we obtain the generalized output synchronization for discrete-time dynamical networks with nonidentical nodes by an appropriate switching among several communication topologies. Finally, two examples are provided to demonstrate the effectiveness of the main results.
ABSTRACT
In this work, we investigate the output synchronization problem for discrete-time dynamical networks with identical nodes. Firstly, if each node of a network is geometrically incrementally dissipative, the entire network can be viewed as a geometrically dissipative nonlinear system by choosing a particular input-output pair. Then, based on the geometrical dissipativity property, we consider two cases: output synchronization under arbitrary topology and switching topology, respectively. For the first case, we establish several criteria of output synchronization under arbitrary switching between a set of connection topologies by employing a common Lyapunov function. For the other case, we give the design method of a switching signal to achieve output synchronization even if all subnetworks are not synchronous. Finally, an example is provided to illustrate the effectiveness of the main results.
