Improved Algorithm for Set Inversion With Application to a Jet Engine Control System

We present an algorithm to characterize the set $S={x∊Rl:f(x)>0}=f−1(]0,∞[m)$ in the framework of set inversion using interval analysis. The proposed algorithm improves on the algorithm of Jaulin et al. (Jaulin, L., Kieffer, M., Didrit, O., and Walter, E., 2001, Applied Interval Analysis, Springer, London). The improvements exploit the powerful tool of monotonicity. We test and compare the performance of the proposed algorithm with that of Jaulin et al. in characterizing the domain of robust stability for the speed control loop of a jet engine. The results of testing show that the proposed algorithm encloses $S$ more accurately, meaning that it gives a larger region of compensator parameter values for which the system stability is guaranteed and a smaller region of the same for which the system stability is indeterminate.