Open AccessJournal Article
Existence of a nonpositive solution to riccati equation
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This article is published in IEEE Transactions on Automatic Control.The article was published on 1974-01-01 and is currently open access. It has received 48 citations till now. The article focuses on the topics: Algebraic Riccati equation & Riccati equation.read more
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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.
Journal ArticleDOI
Nonoptimality of the steady-state cruise for aircraft
TL;DR: In this article, a second-order variational analysis using a frequency-domain version of the classical Jacobi optimality condition is proposed to improve fuel efficiency of cycle cruise paths.
Journal ArticleDOI
Values and strategies for infinite time linear quadratic games
TL;DR: In this paper, it was shown that an appropriate solution of an algebraic Riccati type equation determines the value of the game but not necessarily any equilibrium strategies for a class of infinite time linear quadratic games.
Proceedings ArticleDOI
On quadratic differential forms
TL;DR: In this article, the authors introduce some basic notation for quadratic differential forms and provide a new result regarding the existence of a nonnegative storage function for non-negative storage functions.
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Kalman-Popov-Yakubovich lemma and the S-procedure: A historical essay
S. V. Gusev,A. L. Likhtarnikov +1 more
TL;DR: A history of the Kalman-Popov-Yakubovich lemma and the theorem of losslessness of the S-procedure can be found in this article, where a review of the studies directly concerned with these statements are reviewed.
References
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Journal ArticleDOI
Least squares stationary optimal control and the algebraic Riccati equation
TL;DR: In this paper, the optimal control of linear systems with respect to quadratic performance criteria over an infinite time interval is treated, and the integrand of the performance criterion is allowed to be fully quadratically in the control and the state without necessarily satisfying the definiteness conditions which are usually assumed in the standard regulator problem.
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Algebraic properties of minimal degree spectral factors
TL;DR: The paper derives a result connecting frequency-domain and time-domain properties of different spectral factors of the one power spectrum matrix, interpreted from an algebraic point of view, and applied to the linear-quadratic optimal control and filtering problem.