Real-time integration formulas with off-step inputs and their stability (Q1120965)

Real-time simulations require the numerical integrations of equations of the form \(dy/dt=f(y,u)\), where the vector y contains the variables being numerically simulated (output) and the vector u contains inputs to the numerical integrator from a physical system. The values of u are sampled at a fixed clock rate and similarly y is transferred to the physical system at a fixed clock rate. Even if the system under simulation has no inbuilt delay, the numerical simulation introduces delays. First, some time is required to compute numerically the output to a given input. Second, changes in u are not felt by the integrator until the next u- sampling time. Delays are smaller if the sampling times for u and y are different, a situation that requires a numerical integration formula which uses off-step u information. The authors study the stability of several formulae of this type.