Linear Algebra-Based Multivariable Controller Design for Gas Turbine Machines with State-Derivative Feedback

This paper presents a linear algebra-based control algorithm for multivariable gas turbine systems using matrix polynomial theory and the Kronecker product to assign block roots (i.e., block eigenvectors with prescribed latent structure). State and state-derivative feedback strategies are investigated and validated through simulations on an industrial gas turbine machine. The proposed method enables direct assignment of block roots governing closed-loop stability and transient response, while block eigenvectors shape the dynamic behavior of key turbine variables. Applicability of the approach requires block controllability and/or block observability, ensuring analytical transparency, design flexibility, and effectiveness for multivariable gas turbine control.