Journal ArticleDOI
Pole assignment via Sylvester's equation
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TLDR
In this article, it was shown that the pole assignment problem can be reduced to solving the linear matrix equations AX − XA = −BG, FX = G successively for X, and then F for almost any choice of G.About:
This article is published in Systems & Control Letters.The article was published on 1982-01-01. It has received 202 citations till now. The article focuses on the topics: Assignment problem.read more
Citations
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Journal ArticleDOI
A recurrent neural network for solving Sylvester equation with time-varying coefficients
TL;DR: The recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time-varying solution of a given Sylvester equation.
Journal ArticleDOI
Accelerating a Recurrent Neural Network to Finite-Time Convergence for Solving Time-Varying Sylvester Equation by Using a Sign-Bi-power Activation Function
Shuai Li,Sanfeng Chen,Bo Liu +2 more
TL;DR: A sign-bi-power activation function is proposed in this paper to accelerate Zhang neural network to finite-time convergence and the proposed strategy is applied to online calculating the pseudo-inverse of a matrix and nonlinear control of an inverted pendulum system.
Book
Numerical methods for linear control systems
Daniel Boley,Biswa Nath Datta +1 more
TL;DR: The design and analysis of linear control systems and matrix equations problems, (Lyapunov equations, Sylvester equations, the algebraic Riccati equations), the pole-placement problems, stability problems, and frequency response problems, have been studied.
Journal ArticleDOI
Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment
Biswa Nath Datta,Yousef Saad +1 more
TL;DR: In this article, an Arnoldi-based numerical method for solving a Sylvester-type equation arising in the construction of the Luenberger observer is proposed, where given an N × N matrix A and an n × m matrix G, the method simultaneously constructs an m × m Hessenberg matrix H with a pre-assigned spectrum and an X × m orthonormal matrix X such that AX − XH = G.
Journal ArticleDOI
Robust and well‐conditioned eigenstructure assignment via sylvester's equation
TL;DR: In this article, an algorithmic solution is given for the problem of calculating a pole assignment matrix F that makes the eigenvector matrix of A + BF well-conditioned with respect to inversion, or equivalently, maximally orthonormal.
References
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Journal ArticleDOI
Solution of the matrix equation AX + XB = C [F4]
R. H. Bartels,G. W. Stewart +1 more
TL;DR: The algorithm is supplied as one file of BCD 80 character card images at 556 B.P.I., even parity, on seven ~rack tape, and the user sends a small tape (wt. less than 1 lb.) the algorithm will be copied on it and returned to him at a charge of $10.O0 (U.S.and Canada) or $18.00 (elsewhere).
Journal ArticleDOI
A Hessenberg-Schur method for the problem AX + XB= C
TL;DR: A new method is proposed which differs from the Bartels-Stewart algorithm in that A is only reduced to Hessenberg form, and the resulting algorithm is between 30 and 70 percent faster depending upon the dimensions of the matrices A and B.
Proceedings ArticleDOI
On the flexibility offered by state feedback in multivariable systems beyond closed loop eigenvalue assignment
TL;DR: In this article, a characterization of all closed loop eigenvector sets which can be obtained with a given set of distinct closed-loop eigenvalues using state feedback is given.
Book ChapterDOI
Linear Multivariable Control
TL;DR: These lectures are devoted to qualitative aspects of the design of linear time-invariant multivariable control systems of finite dynamic order, and consider problems of structure and synthesis which have been solved only quite recently.
Journal ArticleDOI
Comments "On pole assignment in multi-input controllable linear systems"
Michael Heymann,W. Wonham +1 more
TL;DR: In this article, a short and direct new proof is given to Wonham's theorem that a time invariant multi-input linear dynamical system is controllable only if its poles can arbitrarily be reassigned in a closed-loop system by means of a constant (state variable) feedback law.