114 research outputs found
Functional observer design using linear matrix inequalities
© 2016, Allerton Press, Inc.It is shown that the problem of observer design for estimating a set of linear combinations of state variables of a plant can be formulated in terms of linear matrix inequalities. An algorithm for constructing functional observers is proposed based on a nonsingular transformation of a plant model in the state space by matrix canonization with subsequent solution of the system of linear matrix inequalities
The Necessary and Sufficient Conditions for Representing Lipschitz Bivariate Functions as a Difference of Two Convex Functions
In the article the necessary and sufficient conditions for a representation
of Lipschitz function of two variables as a difference of two convex functions
are formulated. An algorithm of this representation is given. The outcome of
this algorithm is a sequence of pairs of convex functions that converge
uniformly to a pair of convex functions if the conditions of the formulated
theorems are satisfied. A geometric interpretation is also given
The maximum modulus of a trigonometric trinomial
Let Lambda be a set of three integers and let C_Lambda be the space of
2pi-periodic functions with spectrum in Lambda endowed with the maximum modulus
norm. We isolate the maximum modulus points x of trigonometric trinomials T in
C_Lambda and prove that x is unique unless |T| has an axis of symmetry. This
permits to compute the exposed and the extreme points of the unit ball of
C_Lambda, to describe how the maximum modulus of T varies with respect to the
arguments of its Fourier coefficients and to compute the norm of unimodular
relative Fourier multipliers on C_Lambda. We obtain in particular the Sidon
constant of Lambda
Functional observer design using linear matrix inequalities
© 2016, Allerton Press, Inc.It is shown that the problem of observer design for estimating a set of linear combinations of state variables of a plant can be formulated in terms of linear matrix inequalities. An algorithm for constructing functional observers is proposed based on a nonsingular transformation of a plant model in the state space by matrix canonization with subsequent solution of the system of linear matrix inequalities
Application of Matrix Decompositions for Matrix Canonization
© 2019, Pleiades Publishing, Ltd. Abstract: The problem of solving overdetermined, underdetermined, singular, or ill conditioned SLAEs using matrix canonization is considered. A modification of an existing canonization algorithm based on matrix decomposition is proposed. Formulas using LU decomposition, QR decomposition, LQ decomposition, or singular value decomposition, depending on the properties of the given matrix, are obtained. A method for evaluating the condition number of the canonization problem is proposed. It is based on computing the norm of the matrices obtained as a result of canonization; this method does not require the original matrix to be inverted. A general step-by-step matrix canonization algorithm is described and implemented in MATLAB. The implementation is tested on a set of 100 000 randomly generated matrices. The testing results confirmed the validity and efficiency of the proposed algorithm
Functional observer design using linear matrix inequalities
© 2016, Allerton Press, Inc.It is shown that the problem of observer design for estimating a set of linear combinations of state variables of a plant can be formulated in terms of linear matrix inequalities. An algorithm for constructing functional observers is proposed based on a nonsingular transformation of a plant model in the state space by matrix canonization with subsequent solution of the system of linear matrix inequalities
Application of Matrix Decompositions for Matrix Canonization
© 2019, Pleiades Publishing, Ltd. Abstract: The problem of solving overdetermined, underdetermined, singular, or ill conditioned SLAEs using matrix canonization is considered. A modification of an existing canonization algorithm based on matrix decomposition is proposed. Formulas using LU decomposition, QR decomposition, LQ decomposition, or singular value decomposition, depending on the properties of the given matrix, are obtained. A method for evaluating the condition number of the canonization problem is proposed. It is based on computing the norm of the matrices obtained as a result of canonization; this method does not require the original matrix to be inverted. A general step-by-step matrix canonization algorithm is described and implemented in MATLAB. The implementation is tested on a set of 100 000 randomly generated matrices. The testing results confirmed the validity and efficiency of the proposed algorithm
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