Finite frequency tests for robust performance of systems with real parameter uncertainty

Single-input single-output (SISO) plant families with linear real parameter uncertainty in the numerator and denominator of their transfer functions are considered. It is assumed that the controller has been chosen and a bound given on the sensitivity. A finite test for checking robust performance is developed. It is shown that for SISO plant families with linear uncertainty, performance objectives can be checked by finite tests involving a finite number of frequencies. The one-, two-, and three-parameter cases are treated in detail and the general case is commented upon. The discussion focuses on tracking but other problems can be formulated in this manner and solved