A simple solution to the optimal eigenvalue assignment problem

Abstract

The problem of the optimal eigenvalue assignment for multiinput linear systems is considered. It is proven that for an n-order system with m independent inputs, the problem is split into the following two sequential stages. Initially, the n 0 m eigenvalues are assigned using an n 0 m-order system. This assignment is not constrained to satisfy optimality criteria. Next, an m-order system is used to assign the remaining m eigenvalues in such a way that linear quadratic optimal criteria are simultaneously satisfied. Therefore, the original n-order optimal eigenvalue assignment problem is reduced to an m-order optimal assignment problem. Moreover, the structure of the equivalent m-order system permits further simplifications which lead to solutions obtained by inspection.

Robust model order reduction technique for MIMO systems via ANN‐LMI‐based state residualization

“…To demonstrate the proposed method of MOR, we will consider the dynamical model of a two-area power system presented and illustrated in [27]. The system is a seventh-order model with two inputs and two outputs.…”

“…x =Âx +Bu (35) y =Ĉx +Du (36) where the transformed system matrices are: = P −1 A P,B = P −1 B,Ĉ = C P, andD = D. Notice that = P −1 A P is the left-hand side of Equation (27). In addition, is defined in Equation (29) as an upper triangular matrix which is forced to have the original system eigenvalues as its diagonal elements.…”

Synthesis of decoupling laws for attitude stabilization of a spacecraft

“…This case is considered in many studies (e.g., see [22][23][24][25]). Let us formulate and prove two propositions that the basis for the approach proposed in this study.…”

Genetic algorithm approach with frequency selectivity for model order reduction of MIMO systems

“…A two-area power system is considered in this example [34]. The system is a seventh-order model with two inputs and two outputs.…”