State Control Design of Ostensible Metzler Linear Systems with Unsigned Input Parameters

Abstract

This paper deals with the design of a complete state control for input unsigned, rank deficient matrix parameters of a linear system with system dynamics defined by ostensible structures of Metzler matrices. The proposed solution is based on the principle of diagonal stabilization of positive systems and uses a stabilizing additional component over the decomposition of the Metzler matrix in solving the incomplete internal positivity of such linear system structures. The novelty of the proposed approach is the unified representation of the parametric constraints of the Metzler matrix and the structurally constrained system inputs using linear matrix inequalities, which guarantees that the closed-loop system will be asymptotically stable. Despite the complexity of the constraint conditions on this class of linear continuous systems, the design conditions are formulated using sharp linear matrix inequalities only. A detailed design process is presented using a system-linearized mathematical model to verify the superiority and practicality of the proposed method.