An Efficient Algorithm for Approximating Impulse Inputs and Transferring Instantly the State of Linear Matrix Control Systems

Last decades, the control and system theory has been beneficed more by the new technological trends. Thus, in numerous (computational) applications, for instant in electronics, in computers, in engineering, as well as, in financial issues, some elements of the control and system theory have been introduced. In this paper, we are interested to change instantly the state of linear matrix differential systems into zero time by using very appropriate inputs. Thus, our desired inputs are chosen to be sequences of Dirac function and its derivatives. A new algorithmic method for the approximation of the Dirac sequence and the calculations of the relative matrix coefficients is introduced. This approach extends further our knowledge to this issue.

[1]  A. Zemanian Distribution Theory and Transform Analysis; An Introduction to Generalized Functions, With Applications , 1965 .

[2]  Jeffrey M. Bowen,et al.  Delta function terms arising from classical point‐source fields , 1994 .

[3]  R. Penrose A Generalized inverse for matrices , 1955 .

[4]  B. Datta Numerical methods for linear control systems : design and analysis , 2004 .

[5]  A. D. Karageorgos,et al.  Changing the state of a linear differential system in (almost) zero time by using distributional input function , 2007 .

[6]  E. Squires Analytic Functions and Distributions in Physics and Engineering , 1970 .

[7]  Someshwar Chander Gupta,et al.  Transform and State Variable Methods in Linear Systems , 1966 .

[8]  Alexandros A. Zimbidis,et al.  A generalized linear discrete time model for managing the solvency interaction and singularities arising from potential regulatory constraints imposed within a portfolio of different insurance products , 2008 .

[9]  Athanasios A. Pantelous,et al.  Simulate the State Changing of a Descriptor System in (Almost) Zero Time Using the Normal Probability Distribution , 2008, Tenth International Conference on Computer Modeling and Simulation (uksim 2008).

[10]  Nicos Karcanias,et al.  Zero time adjustment of initial conditions and its relationship to controllability subspaces , 1979 .

[11]  Ivan N. Kirschner,et al.  Approximating the Dirac distribution for Fourier analysis , 1991 .

[12]  A. V. Metcalfe,et al.  Optimal Control, Expectations and Uncertainty. , 1991 .

[13]  R. Kanwal Generalized Functions: Theory and Applications , 2004 .

[14]  S. C. Gupta,et al.  Changing the State of a Linear System by use of Normal Function and its Derivatives , 1963 .

[15]  David A. Kendrick,et al.  Stochastic control for economic models: past, present and the paths ahead , 2005 .

[16]  T. Boykin Derivatives of the Dirac delta function by explicit construction of sequences , 2003 .

[17]  Adi Ben-Israel,et al.  Generalized inverses: theory and applications , 1974 .

[18]  A. Tustin The mechanism of economic systems : an approach to the problem of economic stabilization from the point of view of control-system engineering , 1954 .

[19]  Richard M. Murray,et al.  Panel on Future Directions in Control, Dynamics, and Systems , 2000 .