Computation of a matric convolution-integral that arises in discrete-time DAC theory, and similarly in Discrete/Continuous (D/C) control theory
C.D. Johnson · 2009
In the theory and applications of, the Discrete Time version of, Disturbance-Accommodating (Rejection) Control (DAC), and also in Discrete/Continuous (D/C) Control, there arises a new, novel form of a matric convolution-integral containing "dual-kernels " that evolve in a "counterflow " manner. In general, the effective computation of that matrix, which we have called a ''dual-kernel/counterflow matric convolution integral"presents some challenging problems in the field of computational-control. In this paper, we show that the "dual-kernel/counterflow matric convolution integral" obeys a simple, non-homogenous, linear matric differential equation of first-order, with zero initial-condition which can be re-written as a homogenous coupled-pair of first order matric differential equations. Those matric differential equations provide effective numerical-computation tools using existing algorithms incorporated in commercial software programs such as MATLAB, MATHCAD, etc.