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The core invertibility of a companion matrix and a Hankel matrix
Linear and Multilinear Algebra, 2018ABSTRACTIn this paper, we show that the lower companion matrix associated with the monic polynomial over a ring with unity is core invertible if and only if there exist solutions x and y to (i) , (ii) , (iii) , (iv) In addition, some methods of characterizing and computing the core inverse of a Hankel matrix and a Toeplitz matrix over a field are ...
Jianlong Chen, Tingting Li
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System Approximation via Restructured Hankel Matrix
Circuits, Systems, and Signal Processing, 2021This paper presents a modified minimal realization technique to reduce single input single output (SISO) systems from higher-order SISO systems. The reduction process is based on restructuring the Hankel matrix, which consists of two major elements, i.e., Time Moments and Markov parameters.
R. S. Sengar +2 more
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Approximate realization based upon an alternative to the Hankel matrix: the Page matrix
Systems & Control Letters, 1982The Ho-Kalman algorithm creates a minimum realization of a system, when given a series of deterministic Markov parameters. However, when such a 'truncated' series of Markov parameters has been disturbed with noise, an approximating Hankel matrix has to be constructed for applying the realization algorithm.
P.M.J. Van den Hof +2 more
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Complex Analysis and Operator Theory, 2010
This paper continues recent investigations started in Dyukarev et al. (Complex anal oper theory 3(4):759–834, 2009) into the structure of the set \({\mathcal{H}_{q,2n}^{\ge}}\) of all Hankel nonnegative definite sequences, \({(s_{j})_{j=0}^{2n}}\), of complex q × q matrices and its important subclasses \({\mathcal{H}_{q,2n}^{\ge,{\rm e}}}\) and ...
Bernd Fritzsche +2 more
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This paper continues recent investigations started in Dyukarev et al. (Complex anal oper theory 3(4):759–834, 2009) into the structure of the set \({\mathcal{H}_{q,2n}^{\ge}}\) of all Hankel nonnegative definite sequences, \({(s_{j})_{j=0}^{2n}}\), of complex q × q matrices and its important subclasses \({\mathcal{H}_{q,2n}^{\ge,{\rm e}}}\) and ...
Bernd Fritzsche +2 more
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Hankel matrix transformation of the Walsh–Fourier series
Applied Mathematics and Computation, 2013The Hankel matrix has various applications. In this paper we prove that Hankel matrix is strongly regular and apply to obtain the necessary and sufficient conditions to sum the Walsh-Fourier series of a function of bounded variation.
Mohammed A. Alghamdi, Mohammad Mursaleen
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A Hankel matrix approach to stochastic model reduction
IEEE Transactions on Automatic Control, 1985A procedure for stochastic model reduction is Presented utilizing the Hankel matrix results of Adamjan, Arov, and Krein in a way not previously exploited. It is shown thai the error variance of the resulting N th-order approximation is bounded from above by the N + 1 singular value of the system's Hankel matrix.
A. Frazho, B. Bacon
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Hankel matrix-based denoising for statistical damage diagnosis
2022ISBN:978-84-09-44336 ...
Gres, Szymon +3 more
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Hankel Matrix and Singular Value Decomposition [PDF]
, 1990 This chapter constructs a Hankel matrix from auto-covariance matrices of time series which are used in Chapter 9 to estimate system matrices in the state space models for the data-generating processes. This chapter describes several concepts and relations needed in the later chapters.
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Controllability indices, observability indices and the Hankel matrix
International Journal of Control, 1981A procedure is presented for determining the controllability indices and the observability indices of a linear, time-invariant, strictly proper, controllable and observable system from the truncated Hankel matrix.
George P. Kafiris, Trifon G. Koussiouris
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On Hankel Matrix Approximations and Stochastic Model Reduction
IFAC Proceedings Volumes, 1985Abstract A procedure for stochastic model reduction is presented by using the Hankel matrix results of Adamjan, Arov and Krein. It is shown that the error of the resulting Mth-order approximation is bounded from above by the M + 1 singular value of the system's Hankel matrix.
B.J. Bacon, A.E. Frazho
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