A computational method for determining strong stabilizability of \(n\)-D systems (Q1300577)

The stability of a multidimensional system with transfer function \(p(z)= f(z)/g(z)\), where \(z= (z_1,\dots, z_n)\in\mathbb{C}^n\), is determined by the condition that there exist two complex polynomials \(h\), \(k\) such that \[ k(z)\neq 0,\quad f(z)h(z)+ g(z)k(z)\neq 0 \] for all \(z\) in the unit polydisc \(U\). This has been shown to be equivalent to the winding number of \(g(\gamma)\) being zero for any closed curve \(\gamma\) in \(\overline U\cap \{z\in\mathbb{C}^n: f(z)= 0\}\). This means that efficient computational algorithms are needed to evaluate the winding number. This is achieved in this paper by determining an appropriate discretization of a given cycle.