On the radius of parity interlacing property of plant family with parameter uncertainty

The robust stabilization problem (RSP) associated with a plant family 𝒫(s,δ_) having a parameter uncertainty δ_ is considered. An apparent necessary solvability condition is that every element in 𝒫(s,δ_) is stabilizable. It is shown that this RSP is equivalent to a strong stabilization problem associated with a related plant family 𝒢(s,δ_), and 𝒫(s,δ_) is stabilizable if and only if 𝒢(s,δ_) is as well. Another necessary solvability condition is established in terms of the parity interlacing property of each element in 𝒢(s,δ_) from the viewpoint of strong stabilization. The concept of the radius of the parity interlacing property is introduced. Some computational aspects of this radius are discussed