Search results for "Identity matrix"
showing 6 items of 6 documents
Explicit solutions for a system of coupled Lyapunov differential matrix equations
1987
This paper is concerned with the problem of obtaining explicit expressions of solutions of a system of coupled Lyapunov matrix differential equations of the typewhere Fi, Ai(t), Bi(t), Ci(t) and Dij(t) are m×m complex matrices (members of ℂm×m), for 1≦i, j≦N, and t in the interval [a,b]. When the coefficient matrices of (1.1) are timeinvariant, Dij are scalar multiples of the identity matrix of the type Dij=dijI, where dij are real positive numbers, for 1≦i, j≦N Ci, is the transposed matrix of Bi and Fi = 0, for 1≦i≦N, the Cauchy problem (1.1) arises in control theory of continuous-time jump linear quadratic systems [9–11]. Algorithms for solving the above particular case can be found in [1…
Tuning of Extended Kalman Filters for Sensorless Motion Control with Induction Motor
2019
This work deals with the tuning of an Extended Kalman Filter for sensorless control of induction motors for electrical traction in automotive. Assuming that the parameters of the induction motor-load model are known, Genetic Algorithms are used for obtaining the system noise covariance matrix, considering the measurement noise covariance matrix equal to the identity matrix. It is shown that only stator currents have to be acquired for reaching this objective, which is easy to accomplish using Hall-effect transducers. In fact, the Genetic Algorithm minimizes, with respect to the system covariance matrix, a suitable measure of the displacement between the stator currents experimentally acquir…
CKM matrix and fermion masses in the dualized standard model
1997
A Dualized Standard Model recently proposed affords a natural explanation for the existence of Higgs fields and of exactly 3 generations of fermions, while giving at the same time the observed fermion mass hierarchy together with a tree-level CKM matrix equal to the identity matrix. It further suggests a method for generating from loop corrections the lower generation masses and nondiagonal CKM matrix elements. In this paper, the proposed calculation is carried out to 1-loop. It is found first that with the method suggested one can account readily for the masses of the second generation fermions as a `leakage' from the highest generation. Then, with the Yukawa couplings fixed by fitting the…
Recent mathematical approaches to reconstruct phylogenies: A chemosystematist's and botanist's view
1989
Some basic problems of mathematical phylogenetics are discussed. While algorithms regularly depend on the principle of parsimony, some features of phylogenesis interfere with that principle. Nonrandomness of the distribution of mutations as well as the inconstancy of the molecular clock in time and within a given sequence can bias the calculated relationships of closely related taxa. True comparability of sequences is difficult to establish, since this requires defining of homology of positions and of functions of amino acids as well. Parallelism and convergence can give rise to errors in establishing homology. Furthermore, they are difficult to be integrated into a consistent mathematical …
Can the Adaptive Metropolis Algorithm Collapse Without the Covariance Lower Bound?
2011
The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step $n+1$ \[ S_n = Cov(X_1,...,X_n) + \epsilon I, \] that is, the sample covariance matrix of the history of the chain plus a (small) constant $\epsilon>0$ multiple of the identity matrix $I$. The lower bound on the eigenvalues of $S_n$ induced by the factor $\epsilon I$ is theoretically convenient, but practically cumbersome, as a good value for the parameter $\epsilon$ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitly bound the eigenvalues of $S_n$ away …
The smallest singular value of a shifted $d$-regular random square matrix
2017
We derive a lower bound on the smallest singular value of a random d-regular matrix, that is, the adjacency matrix of a random d-regular directed graph. Specifically, let $$C_1<d< c n/\log ^2 n$$ and let $$\mathcal {M}_{n,d}$$ be the set of all $$n\times n$$ square matrices with 0 / 1 entries, such that each row and each column of every matrix in $$\mathcal {M}_{n,d}$$ has exactly d ones. Let M be a random matrix uniformly distributed on $$\mathcal {M}_{n,d}$$ . Then the smallest singular value $$s_{n} (M)$$ of M is greater than $$n^{-6}$$ with probability at least $$1-C_2\log ^2 d/\sqrt{d}$$ , where c, $$C_1$$ , and $$C_2$$ are absolute positive constants independent of any other parameter…