0000000000204517
AUTHOR
Wieslaw Marszalek
showing 8 related works from this author
Walsh function analysis of 2-D generalized continuous systems
1990
The importance of the generalized or singular 2D continuous systems are demonstrated by showing their use in the solution of partial differential equations in two variables. A technique is presented for solving these systems in terms of Walsh functions. The method replaces the solution of a two-variable partial differential equation with the solution of a linear algebraic generalized 2D Sylvester equation. An efficient technique for the recursive solution of the latter equation is offered. All the results apply also in the usual Roesser 2D state-space case. >
Dynamic programming for 2-D discrete linear systems
1989
The authors calculate the optimal control of 2-D discrete linear systems using a dynamic programming method. It is assumed that the system is described with Roesser's state-space equations for which a 2-D sequence of inputs minimizing the given performance criterion is calculated. The method is particularly suitable for problems with bounded states and controls, although it can also be applied for unbounded cases. One numerical example is given. >
Singular distributed parameter systems
1993
The paper deals with the distributed parameter systems described by coupled partial differential equations with singular matrix coefficients. Initial-boundary-value problems are considered in the light of both singular 1d systems theory and the Fourier approach to distributed parameter systems. The method presented in this paper gives the possibility of determining acceptable initial-boundary conditions. An illustrative example is given.
Inversion of matrix pencils for generalized systems
1993
Abstract This paper clarifies the nature of the Leverrier-Faddeev algorithm for generalized and state-space systems. It presents useful diagrams for recursive computation of the coefficients of the characteristic polynomial and the coefficient matrices of the adjoint matrix for various matrix pencils. A simplified case covers recursive equations and diagrams for inversion of the second-order matrix pencil (Es2 + A1s + A0) where E may be singular. The appendix provides two examples of mechanical and heat exchange systems which can be described by the generalized models.
Error analysis of the orthogonal series solution of linear time-invariant systems
1989
Similarities in the error analysis of the polynomial series solution of linear time-invariant systems are pointed out.
Analysis of singular bilinear systems using Walsh functions
1991
The use of Walsh functions to analyse singular bilinear systems is investigated. It is shown that the nonlinear implicit differential system equation may be converted to a set of linear algebraic Lyapunov equations to be solved iteratively for the coefficients of the semistate x(t) in terms of the Walsh basis functions. Solution of the iterative algorithm is uniformly convergent to the exact solution of the algebraic generalised Lyapunov equation of the singular bilinear system. The present method is slightly more complicated than a similar one arising from the analysis of linear singular systems. In fact, it is a hybrid between the analyses of usual linear singular and bilinear regular sys…
Heat exchangers and linear image processing theory
1989
Abstract This paper shows that the transient analysis of some heat exchangers can be derived easily with the linear equations of image processing theory. Partial differential equations of the cross-flow, parallelflow and rotary heat exchangers are considered together with the corresponding discrete models for linear image processing. Some numerical examples show that the nature of the heat and/or mass transfer problems is similar to those of image processing.
Orthogonal functions analysis of singular systems with impulsive responses
1990
Presents a systematic study using piecewise-constant orthogonal functions for the analysis of impulsive responses of singular systems. Walsh and block-pulse functions solutions are examined.