Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Introduction to algorithms
Technical communique: A graph-theoretic method to find decentralized fixed modes of LTI systems
Automatica (Journal of IFAC)
Discrete-time control of continuous systems with approximate decentralized fixed modes
Automatica (Journal of IFAC)
Algebraic Complexity Theory
Decentralized overlapping control of a formation of unmanned aerial vehicles
Automatica (Journal of IFAC)
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Given an interconnected system, this paper is concerned with the time complexity of verifying if any given unrepeated mode of the system is a decentralized fixed mode (DFM). It is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system. It is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication. This work concludes that the identification of distinct decentralized fixed modes (by means of a deterministic algorithm, rather than a randomized one) is computationally very easy, although the existing algorithms for solving this problem would wrongly imply that it is cumbersome. This paper provides not only a complexity analysis, but also an efficient algorithm for tackling the underlying problem.