23 research outputs found
Novel Gramians for linear semistable systems
In this paper, the notions of pseudo Gramians are introduced for linear time-invariant semistable systems, which allow multiple semisimple poles at the origin. The proposed Gramians are the generalizations of standard Gramian matrices defined for asymptotically stable systems, and they can be computed by a set of Lyapunov equations. Furthermore, it is shown that the controllability and observability of a semistable system are indicated by the ranks of the pseudo Gramians, and the controllability and observability energy functions are also characterized using the pseudo Gramians. Additionally, the H2-norm and H∞-norm of a semistable system are analyzed, and then the results are used for the model reduction of semistable systems. Finally, the effectiveness of the methods is illustrated by an example of a gene regulation network
Model Reduction Methods for Complex Network Systems
Network systems consist of subsystems and their interconnections, and provide
a powerful framework for analysis, modeling and control of complex systems.
However, subsystems may have high-dimensional dynamics, and the amount and
nature of interconnections may also be of high complexity. Therefore, it is
relevant to study reduction methods for network systems. An overview on
reduction methods for both the topological (interconnection) structure of the
network and the dynamics of the nodes, while preserving structural properties
of the network, and taking a control systems perspective, is provided. First
topological complexity reduction methods based on graph clustering and
aggregation are reviewed, producing a reduced-order network model. Second,
reduction of the nodal dynamics is considered by using extensions of classical
methods, while preserving the stability and synchronization properties.
Finally, a structure-preserving generalized balancing method for simplifying
simultaneously the topological structure and the order of the nodal dynamics is
treated.Comment: To be published in Annual Review of Control, Robotics, and Autonomous
System