A New Algorithm for Testing the Stability of a Polytope: A Geometric Approach for Simplification

[+] Author and Article Information
Jinsiang Shaw

Department of Mechanical Engineering, Huafan College of Humanities and Technology, Shihtin, Taipei, Taiwan 223

Suhada Jayasuriya

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123

J. Dyn. Sys., Meas., Control 118(3), 611-615 (Sep 01, 1996) (5 pages) doi:10.1115/1.2801188 History: Received October 24, 1990; Online December 03, 2007


Considered in this paper is the robust stability of a class of systems in which a relevant characteristic equation is a family of polynomials F: f(s, q) = a0 (q) + a1 (q )s + [[ellipsis]] + a n (q)sn with its coefficients ai (q) depending linearly on q unknown-but-bounded parameters, q = (p1 , p2 , [[ellipsis]], pq )T . It is known that a necessary and sufficient condition for determining the stability of such a family of polynomials is that polynomials at all the exposed edges of the polytope of F in the coefficient space be stable (the edge theorem of Bartlett et al., 1988). The geometric structure of such a family of polynomials is investigated and an approach is given, by which the number of edges of the polytope that need to be checked for stability can be reduced considerably. An example is included to illustrate the benefit of this geometric interpretation.

Copyright © 1996 by The American Society of Mechanical Engineers
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