Journal ArticleDOI
Simultaneous Stabilizability of Three Linear Systems Is Rationally Undecidable
Vincent D. Blondel,Michel Gevers +1 more
Reads0
Chats0
TLDR
It is shown that the simultaneous stabilizability of three linear systems, that is the question of knowing whether threelinear systems are simultaneously stabilizable, is rationally undecidable.Abstract:
We show that the simultaneous stabilizability of three linear systems, that is the question of knowing whether three linear systems are simultaneously stabilizable, is rationally undecidable. By this we mean that it is not possible to find necessary and sufficient conditions for simultaneous stabilization of the three systems in terms of expressions involving the coefficients of the three systems and combinations of arithmetical operations (additions, subtractions, multiplications, and divisions), logical operations (''and'' and ''or''), and sign test operations (equal to, greater than, greater than or equal to,...).read more
Citations
More filters
Book
Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
DissertationDOI
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
TL;DR: In this paper, the authors introduce a specific class of linear matrix inequalities (LMI) whose optimal solution can be characterized exactly, i.e., the optimal value equals the spectral radius of the operator.
Journal ArticleDOI
Transcendental number theory, by Alan Baker. Pp. x, 147. £4·90. 1975. SBN 0 521 20461 5 (Cambridge University Press)
TL;DR: In this article, the authors give a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients, and their study has developed into a fertile and extensive theory enriching many branches of pure mathematics.
Journal ArticleDOI
Nonsmooth $H_infty$ Synthesis
Pierre Apkarian,Dominikus Noll +1 more
TL;DR: This work develops nonsmooth optimization techniques to solve H_inftysynthesis problems under additional structural constraints on the controller that avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems.
Proceedings ArticleDOI
On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback
Onur Toker,Hitay Özbay +1 more
TL;DR: The main result of this paper shows that the problem of checking the solvability of BMIs is NP-hard, and hence it is rather unlikely to find a polynomial time algorithm for solving general BMI problems.
References
More filters
Book
Real and complex analysis
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Book
Control System Synthesis : A Factorization Approach
TL;DR: In this article, the stable factorization approach is introduced to the synthesis of feedback controllers for linear control systems, where the controller is designed as a matrix over a fraction field associated with a commutative ring with identity, denoted by R, which also has no divisors of zero.
Book
Theory of Functions of a Complex Variable
TL;DR: In this paper, the Laurent series is used for expanding functions in Taylor series, and the calculus of residues is used to expand functions in Laurent series volumes II, III, and IV.
Journal ArticleDOI
Transcendental number theory, by Alan Baker. Pp. x, 147. £4·90. 1975. SBN 0 521 20461 5 (Cambridge University Press)
TL;DR: In this article, the authors give a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients, and their study has developed into a fertile and extensive theory enriching many branches of pure mathematics.