Stability testing for systems with polynomial uncertainty

Proceedings of the American Control Conference - Tập 5 - Trang 3896-3901 vol.5 - 2002
M.S. Fadali1
1Electrical Engineering Department, University of Nevada, Reno, NV, USA

Tóm tắt

We develop a new stability tests for systems with one uncertain parameter and with polynomial uncertainty structure. The test is derived using the resultant determinant for the real and imaginary parts of the polynomial evaluated on the imaginary axis. The resultant determinant is a function of the uncertain parameter as well as frequency. We evaluate the determinant using a known algorithm then test it for roots in a given interval using Sturm's theorem. We apply Sturm's test twice: over the allowable range of the uncertain parameter, and for positive angular frequencies. The procedure yields a necessary and sufficient stability condition with polynomial uncertainty structure and one uncertain parameter. We demonstrate the new test using two numerical examples.

Từ khóa

#System testing #Polynomials #Uncertainty #Frequency #Robust stability #Grid computing

Tài liệu tham khảo

belanger, 1995, Control Engineering A Modern Approach farouki, 2001, Minkowski geometric algebra of complex sets, Geometriae Dedicata, 85, 283, 10.1023/A:1010318011860 gellert, 1989, The VNR Concise Encyclopedia of Mathematics zadeh, 1963, Linear System Theory barmish, 1994, New Tools for Robustness of Linear Systems ackermann, 1993, Robust Control Systems with Uncertain Physical Parameters 10.1080/00207178108922969 bialias, 1985, A necessary and sufficient condition for the stability of convex combinations of stable polynomials or matrices, Bulletin of the Polish Academy of Sciences, 33, 473 10.1016/0005-1098(93)90184-U 10.1109/9.661615 anderson, 1995, Easily testable sufficient conditions for the robust stability of systems with multilinear parameter dependence, Automatica, 31, 25, 10.1016/0005-1098(94)E0049-N 10.1109/9.544011 10.1109/9.53530