A continuous canonical form for static output feedback in linear system

A continuous canonical form for static output feedback (SOF) K in m-input, p-output, n-th order linear system is studied within Grassmannian frame, in the restricted map to closed-loop characteristic polynomial p(s, K) from transfer function matrix. Under the Grassmannian vector formula of closed-loop characteristic polynomial, e(s)Lk (= p(s, K)), all the SOF equivalence classes and their continuous canonical form (CCF) are investigated on the group action of extended real SOF vector k whose elements cover the mp-entries of K as a subset (K ⊂ k), where e(s) = [sⁿ s^n-1 ... s 1] is a basis vector of s variable and L denotes the so-called, Plücker matrix, as a Grassmannian real coefficient matrix of closed-loop charcteristic polynomial. Through the analysis on the graph of group action of k in the product topology, it is proved that the SOF vector equation for system poles Lk = a over arbitrary real coefficient vector a, presents a CCF for SOF pole-assignment on real SOF K. An example is illustrated.