RobustStability ofCityBusSteering Control

Inthispapernewalgorithm forrobust stability analysis oflinear systems withparametric uncertainty is presented. The algorithm is basedon multivariate interpolation-evaluation methodsand fastFourier transform usedforcomputing determinant ofamultivariate polynomial matrix. Positivity ofa multivariate polynomial onahyperrectangle istested byBernstein algorithm. The highefficiency oftheproposed algorithm isdemonstrated on automatic steering control ofDaimler Benzcity bus- an8- thorderclosed-loop system withtwouncertain parameters. Robuststability of polynomials withparametric uncertainty isintensively studied since thecelebrated Kharitonov theorem (KHA,78)hasbeenpublished. Kharitonov solves therobust stability problem for interval continuous-time polynomials. Thesameproblem forpolynomials withparametric uncertainty ofaffine structure issolved bytheEdgetheorem (BAR,88). Mapping theorem (ZAD, 63)showsthat thenon-convex value setofmultilinear interval polynomials iscontained intheconvex polygon given byits vertices. usedforconstant matrices - triangularizatio n and subsequent multiplication oftheelements onthemain diagonal orbysymbolic computations. Thedrawback of bothmethods consists intheir lowefficiency. Evenfor systems ofmoderate order ornumberofparameters the computational timegoestotenths ofseconds. The presented algorithm reduces thecomputational time dramatically.