Hybridized Ackermann’s Methods

Abstract

Further elaborations on the modified Ackermann’s method (MAM) for eigenvalue assignment are considered in this paper. Additional results concerning the incomplete eigenvalue assignment (IEA) are stated, verified, and commented. The advantages of IEA are pursued even further in this study beyond that mentioned in [1]. The study proposes two newly appended approaches based on MAM; named spectral and truncated methods. They are grounded on IEA, which fundamentally exemplify a hybridized approach to eigenvalue assignment. Necessary and sufficient conditions for stability of the truncated hybridized method are established, proved, and validated by examples. All results obtained apply equally-well to identical eigenvalue assignment, complex eigenvalue assignment, as well as to uncontrollable systems. Besides, they lead to simplified state feedback matrix determination. Three numerical examples are fully worked out to substantiate the nature of the IEA and the two hybridized methods. Simulation and visualization using MATLAB demonstrate the flexibility of the proposed methods.