Discrete first-order models for multivariable process control

The concept of an m×m invertible continuous first-order lag is extended to define an equivalent formulation for multivariable sampled-data systems. A large class of proportional-plus-summation-output feedback controllers is constructed. Each controller guarantees the stability of the closed-loop system and, also, low-closed-loop interaction effects if the sampling rate is high enough. The results are extended to show that a multivariable discrete first-order lag is, 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 a nonsingular value of CB will satisfy the contraction condition provided that the sampling rate is high enough.