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

Abstract

The robust stabilization problem (RSP) associated with a plant family /spl Pscr/(s,/spl delta/_) having a parameter uncertainty /spl delta/_ is considered. An apparent necessary solvability condition is that every element in /spl Pscr/(s,/spl delta/_) is stabilizable. It is shown that this RSP is equivalent to a strong stabilization problem associated with a related plant family /spl Gscr/(s,/spl delta/_), and /spl Pscr/(s,/spl delta/_) is stabilizable if and only if /spl Gscr/(s,/spl delta/_) is as well. Another necessary solvability condition is established in terms of the parity interlacing property of each element in /spl Gscr/(s,/spl delta/_) 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.