Partial eigenvalue assignment of descriptor fractional discrete-time linear systems by parametric state feedback

Document Type : Research Paper


Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.


In this paper, we present a nonlinear parametric method to stabilize descriptor fractional discrete time linear system practically. Parametric methods with the free parameters can be adjusted to obtain better performance responses like minimum norm in state feedback. The aim is assigning desirable eigenvalues to obtain satisfactory responses by forward state feedback and forward and propositional state feedback in new systems with large matrices. However, finding the solution to nonlinear parametric equations makes some errors. In partial eigenvalue assignment, just a part of the open-loop spectrum of the standard linear systems is reassigned, while leaving the rest of the spectrum invariant. The size of matrices, state, and input vectors are decreased and the stability is kept. At the end, summary and conclusions are proposed and the convergence of state vectors in the descriptor fractional discrete-time system to zero is also shown by figures in a numerical example. Our method is also compared with another method with one of orthogonality relations in our article and example.