Analysis of uncertain transfer functions in factored form

It is well known that the mathematical representations of real physical systems suffer from parametric uncertainty due to modelling errors, nonlinearities, manufacturing tolerances and operating conditions. Therefore, it is very important to take parametric variations into account while analysing and designing control systems. This paper presents some results for computation of the robust stability of control systems with an uncertain transfer function in factored form which is the form of most real physical systems. The technique presented uses the narrowest possible Bode envelopes, which are constructed from new results obtained by the authors, and therefore it can be used for the stability analysis and design of robust controllers to meet certain closed loop stability and performance requirements for such systems less conservatively than other methods. The importance of the method for the computation of stability is discussed and illustrative examples are given.