Discrete First-Order Models for Multi-variable Process Control

The concept of an mxm invertible continuous first order lag is extended to define an equivalent formulation for multi-variable sampled-data-systems. A large class of proportional plus summation output feedback controllers is constructed. Each controller guarantees the stability of the closed-loop interaction effects if the sampling rate is high enough. The results are extended to show that a multi-variable discrete first order lag, in many cases of practical interest, a quite adequate approximation for the purpose of controller design provided that the plant is minimum-phase and satisfies a contraction-mapping condition. In particular, any discrete model of a minimum phase, continuous, linear, time-invariant plant with CB nonsingular will satisfy the contraction condition provided the sampling rate is high enough.