Pole structure assignment via non-regular static state feedback
The authors study the problem of transmission pole structure assignment by the non-regular static state feedback \(u= Fx+ Gv\) for linear, time-invariant systems \(\dot x= Ax+ Bu\), where \(A\), \(B\), \(F\), \(G\) are real matrices. They prove a necessary and sufficient condition for a given list of polynomials \(\psi_1(s)\geq \psi_2(s)\geq\cdots\geq \psi_p(s)\) to give the transmission pole structure of the closed-loop system \(\dot x= (A+ BF)x+ BGv\). The condition involves the calculation of the infimal set of the controllability indices the system can attain through feedback while satisfying the Rosenbrock inequalities. The authors use some lattice properties of finite lists of integers to solve the problem.
infimal set of the controllability indices
scientific article; zbMATH DE number 1353723
scientific article