Output control of the spectrum of a linear dynamic system in terms of the Van der Woude method

An efficient method is developed for the output control of the spectrum of a linear dynamic system given in a state space. The method is developed by extending the Van der Woude approach to multiple-input multiple-output systems and by applying a novel multilevel decomposition based on matrix zero divisors. The method is universal in the sense that, without any modification, it applies to both continuous- and discretetime systems. Under the solvability conditions, the method has no restrictions on the algebraic multiplicity of spectral elements and yields analytical solutions of the regulator synthesis problem.