Hard Problems in Linear Control Theory: Possible Approaches to Solution
Automation and Remote Control
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Automatica (Journal of IFAC)
A new exclusion test for finding the global minimum
Journal of Computational and Applied Mathematics
Automation and Remote Control
Simultaneous control of linear systems by state feedback
Computers & Mathematics with Applications
Advanced Engineering Informatics
H∞ structured model reduction algorithms for linear discrete systems via LMI-based optimisation
International Journal of Systems Science
Implementation of FIR control for H∞output feedback stabilization of linear systems
ACC'09 Proceedings of the 2009 conference on American Control Conference
ACC'09 Proceedings of the 2009 conference on American Control Conference
Switched systems reduction framework based on convex combination of generalized gramians
Journal of Control Science and Engineering
Distributed estimation over complex networks
Information Sciences: an International Journal
Randomized algorithms for robust controller synthesis using statistical learning theory
Automatica (Journal of IFAC)
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
Observer-based stabilization of switching linear systems
Automatica (Journal of IFAC)
Brief Probabilistic solutions to some NP-hard matrix problems
Automatica (Journal of IFAC)
Static H∞ loop shaping control of a fly-by-wire helicopter
Automatica (Journal of IFAC)
Uniform stabilization of discrete-time switched and Markovian jump linear systems
Automatica (Journal of IFAC)
Verifiable conditions on asymptotic stabilisability for a class of planar switched linear systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Atomic optimization. I. Search Space Transformation and One-dimensional Problems
Automation and Remote Control
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We show that some basic linear control design problems are NP-hard, implying that, unless P=NP, they cannot be solved by polynomial time algorithms. The problems that we consider include simultaneous stabilization by output feedback, stabilization by state or output feedback in the presence of bounds on the elements of the gain matrix, and decentralized control. These results are obtained by first showing that checking the existence of a stable matrix in an interval family of matrices is NP-hard.