Graphical stability robustness tests for linear time-invariant systems: generalizations of Kharitonov´s stability theorem

The authors derive two graphical tests for the U-Hurwitz stability of convex polyhedra of polynomials. The first is a Nyquist-type test, which has been extended to arbitrary connected sets of polynomials. The second is a root-locus-type test, previously known as the edge theorem. A finite test based on the root-locus-type result is developed. All results are extended to distributed-parameter systems. For the polyhedral case, although the root-locus-type test has a finite implementation, it is concluded that the Nyquist-type test will in general be more useful. The analysis is motivated by an elementary proof of Kharitonov´s stability theorem