On the Stability and Robust Stability of Networked Dynamic Systems

Abstract

Some necessary and sufficient conditions are derived for the stability of a networked system with linear time invariant dynamics. Connections among its subsystems are fixed but arbitrary, and every subsystem can have different dynamics. Based on these results, some necessary or sufficient conditions are further obtained for both its stability and robust stability, which essentially depend only on parameter matrices of each individual subsystem and the subsystem connection matrix. This characteristic makes them attractive in the analysis and synthesis of a large scale networked system.

Minimal Inputs/Outputs for a Networked System

“…As a further topic, it is interesting to see whether or not these results can be extended to situations in which there are some other structure restrictions on the system input/output matrix, which is often met in practical applications [6], [13], as well as to situations in which subsystems are connected through their outputs like those discussed in [17], [18]. The latter is thought to be a more natural way in describing dynamics of a large scale system.…”

“…With the development of network and communication technologies, etc., various new challenging theoretical issues arise in the analysis and synthesis of a networked system, which can be regarded as one special kind of large scale systems that have attracted extensive research interests since almost half a century ago [8], [12], [17], [18]. Some examples are efficient utilization of the structure information like sparsity etc., in reducing computational costs in distributed estimation and control, analysis for their stability, controllability, observability [2], [5], [6], [7], [17].…”

Minimal inputs/outputs for subsystems in a networked system

“…With the increment of the dimension of a system, which is mainly due to technology developments in sensors, communications, etc., as well as more complicated and demanding tasks expected for a system, computation costs and numerical stability emerge as essential issues in system analysis and synthesis [9], [13], [17], [21]. It is now widely recognized that with the increment of its subsystem number, direct applications of results about a lumped system to a large scale or networked system may often result in an exponential increment of computation time and storage requirements [2], [4], [9], [13], [17].…”

Distributed observer design for networked dynamical systems

“…Without loss of generality, it is assumed that every row of the matrix Φ has only one nonzero element which is equal to one [11]. From [16] …”

“…In [16], a computationally attractive necessary and sufficient condition is derived for the stability of the networked system Σ as follows.…”