Robust stabilization of plant family with parameter uncertainty and the method of calculating parity interlacing property radius

The robust stabilization of a plant family P (s, δ) having parameter uncertainty is sdudied. The necessary and sufficient conditions of stabilization are given - that some plant family G (s, δ) is stabilizable. There are two conditions for strong stabilization: (1) no unstable zero-pole cancellation; (2) all objectives should satisfy the condition of parity interlacing property (p. i. p.). To ascertain whether a given plant family can be strongly stabilized, the concept of p. i. p. radius is introduced and root locus method is used to analyse the p. i. p. condition and implement the p. i. p. radius calculation.