Plant tuning: A robust Lyapunov approach

We consider the problem of tuning the output of a static plant whose model is unknown, under the only information that the input–output function is monotonic in each component or, more in general, that its Jacobian belongs to a known polytope of matrices. As a main result, we show that, if the polytope is robustly non–singular (or has full rank, in the non–square case), then a suitable tuning scheme drives the output to a desired point. The proof is based on the application of a well known theorem concerning the existence of a saddle point for a min–max zero–sum game. Some application examples are suggested.