A Canonical Form for the Inclusion Principle of Dynamic Systems
SIAM Journal on Control and Optimization
Brief paper: A graph-theoretic characterization of structurally fixed modes
Automatica (Journal of IFAC)
Papers: Algebraic characterization of fixed modes in decentralized control
Automatica (Journal of IFAC)
A new approach to control design with overlapping information structure constraints
Automatica (Journal of IFAC)
Decentralized optimal traffic engineering in connectionless networks
IEEE Journal on Selected Areas in Communications
Overlapping control systems with optimal information exchange
Automatica (Journal of IFAC)
Brief paper: Overlapping control design for multi-channel systems
Automatica (Journal of IFAC)
Brief paper: Robust controllability and observability degrees of polynomially uncertain systems
Automatica (Journal of IFAC)
ACC'09 Proceedings of the 2009 conference on American Control Conference
Hi-index | 22.15 |
This paper deals with the characterization of the fixed modes of multi-channel systems with respect to linear time-invariant (LTI) structurally constrained controllers. Fixed modes can be found numerically for any LTI system with respect to any given control structure, using a random number generator. The existing analytical methods, however, are not capable of characterizing the fixed modes in the most general case of non-strictly proper systems with non-block diagonal (i.e., overlapping) control structure, efficiently. The notion of a decentralized overlapping fixed mode (DOFM) is introduced in this paper to address the above problem in the most general case. To this end, the knowledge of the overlapping control structure is translated into a bipartite graph, whose vertices correspond to the input and output vectors of various control channels. An efficient technique is applied to the obtained graph to identify the DOFMs of the system. It is to be noted that a system is stabilizable via an appropriate LTI decentralized overlapping controller if and only if it does not have any unstable DOFM. Moreover, it is shown how those modes which are not DOFMs can be placed freely in the complex plane using a proper LTI decentralized overlapping controller. The efficacy of this work is demonstrated through an example.