Modelling of uncertain systems via linear programming (Q1914995)

Most industrial control loops are designed using linear time-invariant (LTI) plant models. The authors formalize the problem of best approximate LTI modelling of BIBO-stable linear time-varying (LTV) systems in a way that is compatible with the notion of induced \(l^\infty\) norm used in robust \(l^1\) control. This setup is closely related with identification methods and control-motivated validation/invalidation procedures that can be implemented with special-purpose linear programming (LP) techniques. Results are given for approximate modelling of BIBO-stable LTV and LTI systems, using LTI models. It is shown that such parametrizations are satisfactory from an approximate modelling point of view, and can be used in output-error type LP identification and in LP model validation procedures. Simulation examples are given to illustrate that such techniques give good results to solve problems of realistic size.