Papers: Algebraic characterization of fixed modes in decentralized control
Automatica (Journal of IFAC)
Discrete-time control of continuous systems with approximate decentralized fixed modes
Automatica (Journal of IFAC)
Overlapping control systems with optimal information exchange
Automatica (Journal of IFAC)
Brief paper: Robust controllability and observability degrees of polynomially uncertain systems
Automatica (Journal of IFAC)
Complexity of checking the existence of a stabilizing decentralized controller
ACC'09 Proceedings of the 2009 conference on American Control Conference
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This paper deals with the decentralized pole assignability of interconnected systems by means of linear time-invariant (LTI) controllers. A simple graph-theoretic approach is proposed to identify the distinct decentralized fixed modes (DFMs) of the system, i.e., the unrepeated modes which cannot be moved by means of a LTI decentralized controller. The state-space representation of the system is transformed to the decoupled form using a proper change of coordinates. For any unrepeated mode, a matrix is then computed which resembles the transfer function matrix of the system at some point in the complex plane. A bipartite graph is constructed accordingly in terms of the computed matrix. Now, the problem of verifying if this mode is a DFM of the system reduces to checking if the constructed graph has a complete bipartite subgraph with a certain property. The sole restriction of this work is that it is only capable of identifying the distinct DFMs of a system. However, it is axiomatic that most of the modes of the real-world systems are normally distinct. The primary advantage of the present paper is its simplicity, compared to the existing ones which often require evaluating the rank of several matrices.