China
Africa
Explore chapters and articles related to this topic
Two Decades of Multidimensional Systems Research and Future Trends
Published in Krzysztof Gałkowski, Jeff David Wood, Multidimensional Signals, Circuits and Systems, 2001
Without loss of generality, set atn = 1 for notational brevity. It was pointed out that the Schur complement and Bezoutian matrices, each of which is about half the order of the resultant matrix (Sylvester matrix or inner matrix), could also be used to generate inequalities identical to the inner determinantal polynomial inequalities. The advantage of lower computational complexity is somewhat offset by the need to compute the elements of the matrices by operating on the coefficients. An approach based on the related Sturm-Habicht algorithm was also considered by González-Vega.
Linear Algebra Problems
Published in Dingyü Xue, YangQuan Chen, Scientific Computing with MATLAB®, 2018
The coefficient matrix is the transpose of Sylvester matrix. It can be shown that, if two polynomials A(s) and B(s) are coprime, the Sylvester matrix is nonsingular. Therefore, the equation has a unique solution. To check whether two polynomials are coprime or not, the simplest way is to find the greatest common divisor of the two polynomials and see whether it includes s. If no polynomial is found in greatest common divisor, the two polynomials are coprime.
Blind Channel Identification and Source Separation in Space Division Multiple Access Systems
Published in Lal Chand Godara, Handbook of Antennas in Wireless Communications, 2018
Victor Barroso, João Xavier, José M. F. Moura
For an N × M matrix A = [a1 ⋯ aM] and an integer, J, we let the N(J + 1) × (M + J + 1) matrix τJ(A) denote the block-Sylvester matrix () τJ(A)=[a1⋯aM0⋯00a1⋯aM⋱⋮⋮⋱⋱⋱⋱00⋯0a1⋯aM]
Enclosing the solution set of the parametric generalised Sylvester matrix equation A(p)XB(p) + C(p)XD(p) = F(p)
Published in International Journal of Systems Science, 2019
Marzieh Dehghani-Madiseh, Milan Hladík
For obtaining a tighter enclosure we use a residual technique and some properties of the interval arithmetic which lead to a tighter result. Suppose , so there exists such that . If we set in which is a given m-by-n matrix then Y will be the solution of If the interval matrix is an enclosure for the family then the interval system will be a collection of the generalised Sylvester matrix equations that contains the generalised Sylvester matrix equation (13). So if is an outer estimation for the solution set of , then it is obvious that and hence .
Stability and stabilisation of Itô stochastic systems with piecewise homogeneous Markov jumps
Published in International Journal of Systems Science, 2019
Hui-Jie Sun, Ai-Guo Wu, Ying Zhang
For system (21), condition (27) holds (Fu & Li, 2016). Substituting (28) into (24) gives Denote Then, the equation (29) can be simplified as In fact, the equation (30) is the Sylvester matrix equations. According to Lemma 5.1, if the solutions and of the Sylvester matrix equation (30) is obtained, then the matrices can be computed by (28). Furthermore, the feed-forward compensator gain matrices can be obtained from (26). For the Sylvester matrix equation (30), the following iterative algorithm can be given to find its solutions.
The feedback invariant measures of distance to uncontrollability and unobservability
Published in International Journal of Control, 2022
Nicos Karcanias, Olga Limantseva, George Halikias
Consider the set of (29). We can define matrix associated with : and matrix associated with as: for every . An extended Sylvester matrix or a Sylvester Resultant for the set P is then defined by: