Stability Analysis of Polynomials with Polynomic Uncertainty
Petr Hušek · InTech eBooks · 2008
The algorithm checking robust stability of polynomials with polynomic dependency of its coefficients on vector interval parameter was presented. The method is based on testing the value set in frequency domain. The value set evaluated in a point lying on the boundary of stability region is overbounded by a convex polygon. The zero exclusion test is performed by positivity checking of multivariate polynomic functions using the Bernstein algorithm. The procedure results in sufficient stability condition. The main advantage of the presented algorithm over those based on computation of Hurwitz determinant consists in its capability of treating relatively large problems because of the low requirements on computer storage capacity. Moreover, arbitrary stability region can be chosen. Efficiency of the algorithm was verified on the benchmark example of the Fiat Dedra engine control by comparison with the Bernstein expansion algorithm.