Abstract
We study feedback pole placement for continuous descriptor (generalized state-space) systems depending on parameters, which have the formE(ω)x(t, ω)=A(ω)x(t, ω)+B(ω)u(t, ω).Here, x(t, ω) and u(t, ω) are a descriptor variable and an input, respectively. The entries of the above matrices are real- or complex- valued continuous functions defined on a subspace of a multi-dimensional euclidean space.
Such systems arise in the study of descriptor systems whose coefficients are continuous functions of one or more parameters, neutral delay-differential systems, and spatially-distributed systems in descriptor form.
In the paper, we first define the pointwise-controllability for continuous descriptor systems depending on parameters of the above form. Next, we derive a sufficient and necessary condition for pointwise control lability in terms of a pointwise rank criterion. Then, for pointwise controllable systems, we describe pole placement by the descriptor variable feedback u(t, ω)=f(ω)x(t, ω) using feedback gains that also depend on parameters.
