A Quasi-Decoupling Approach for Nonclassical Linear Systems in State Space

Abstract

By adopting the orthogonal transformations provided by the generalized real Schur decomposition, it is shown that every nonclassical linear system in state space can be transformed into block upper triangular form, to which the quasi-decoupling solution can be progressively carried out by solving the either first or second-order component equations with the “back substitution.” The distinct characteristics of generalized eigenvalue problems from those of standard ones are discussed. Favorable properties of the proposed method include: no inverting of any system matrix, indiscriminate applicability to both defective and nondefective systems, the simultaneous decoupling of the adjoint problem, and numerical stability. Illustrative examples are also presented.