Numerical Evaluation of the “Dual-Kernel, counter-flow” matric convolution integral that arises in Discrete/Continuous (D/C) control theory

Discrete/Continuous (D/C) control theory is a new generalized theory of discrete-time control that expands the concept of conventional (exact) discrete-time control so that actuator commands need not be constant between control decisions, but can be more generally defined and implemented as functions that vary with time across each sample period in some beneficial manner. Because the plant/control system construct contains two linear subsystems arranged in tandem, a novel ldquodual-kernel counter-flowrdquo convolution integral appears in the formulation; and, as part of the D/C control design and implementation process, numerical evaluation of that integral over each sample period is required. Three fundamentally different evaluation methods and associated algorithms are derived for the constant-coefficient case, and numerical results are matched against three available examples that have closed-form solutions.