A minimal basis of identities for a second-order matrix algebra over a field of characteristic o

1981 ◽  
Vol 20 (3) ◽  
pp. 188-194 ◽  
Author(s):  
V. S. Drenski
Keyword(s):  
Matrix Algebra ◽  
Second Order ◽  
Minimal Basis ◽  
Basis Of Identities ◽  
Order Matrix ◽  
Algebra Over A Field

scholarly journals On some properties and special identities in the second order matrix algebra over Grassmann algebras

2013 ◽  
Vol 46 (1) ◽  
Author(s):  
Tsetska Rashkova
Keyword(s):  
Matrix Algebra ◽  
Second Order ◽  
Order Matrix ◽  
Multiplication Property ◽  
Grassmann Algebras ◽  
The Matrix

AbstractThe paper considers the anticommutative multiplication property for the matrix algebra

scholarly journals A Markovian canonical form of second-order matrix-exponential processes

2008 ◽  
Vol 190 (2) ◽  
pp. 459-477 ◽  
Author(s):  
L. Bodrog ◽  
A. Heindl ◽  
G. Horváth ◽  
M. Telek
Keyword(s):  
Canonical Form ◽  
Second Order ◽  
Matrix Exponential ◽  
Order Matrix

scholarly journals Feedback Linearisation for Nonlinear Vibration Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
S. Jiffri ◽  
P. Paoletti ◽  
J. E. Cooper ◽  
J. E. Mottershead
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Problems ◽  
Second Order ◽  
Degree Of Freedom ◽  
Sensors And Actuators ◽  
Order Matrix ◽  
Problem Class ◽  
Aeroelastic Model ◽  
Matrix Differential ◽  
Three Degree Of Freedom

Feedback linearisation is a well-known technique in the controls community but has not been widely taken up in the vibrations community. It has the advantage of linearising nonlinear system models, thereby enabling the avoidance of the complicated mathematics associated with nonlinear problems. A particular and common class of problems is considered, where the nonlinearity is present in a system parameter and a formulation in terms of the usual second-order matrix differential equation is presented. The classical texts all cast the feedback linearisation problem in first-order form, requiring repeated differentiation of the output, usually presented in the Lie algebra notation. This becomes unnecessary when using second-order matrix equations of the problem class considered herein. Analysis is presented for the general multidegree of freedom system for those cases when a full set of sensors and actuators is available at every degree of freedom and when the number of sensors and actuators is fewer than the number of degrees of freedom. Adaptive feedback linearisation is used to address the problem of nonlinearity that is not known precisely. The theory is illustrated by means of a three-degree-of-freedom nonlinear aeroelastic model, with results demonstrating the effectiveness of the method in suppressing flutter.

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