Gain optimization for distributed plants (Q1072979)

Let \(p_ k(s)\) be a continuously parametrised family of linear continuous-time, time-invariant, strictly proper plants, where the parameter k takes values in some compact set K. Consider the problem of designing a proper controller c(s) such that for each k in K the unity feedback system whose forward loop has transference \(c(s)p_ k(s)\) is internally asymptotically stable. For a general discussion of this problem see the second author's textbook [''Invariance and system theory: algebraic and geometric aspects'' (1981; Zbl 0496.93001)]. In the present paper the authors give an explicit solution to the above problem for the special case \(p_ k(s)=k p_ 0(s)\), where \(p_ 0\) is a fixed SISO plant and K is a compact real interval. For \(p_ 0\) finite- dimensional, a complete solution based on Nevanlinna-Pick interpolation techniques is already given in the above reference. In the present paper the authors show that these interpolation techniques extend to a large class of distributed parameter systems.