Stability and performance analysis in an uncertain world

Classical control systems design uses fixed plant transfer functions, yet engineers have known for many years that there is often considerable uncertainty regarding the parameters used in a transfer function representation. A major breakthrough on systems with uncertain parameters was achieved by the Russian mathematician V.L. Kharitonov (1979), who extended the Routh stability criterion to interval polynomials, that is where the polynomial coefficients may be assumed to lie within a specific range rather than being fixed. Recently these ideas have been extended to frequency response representations, such as Nyquist and Bode plots, for interval plant transfer functions. This paper reviews some of these results, which can be easily understood and used by practising engineers.