Stability testing for systems with polynomial uncertainty

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.