Constrained stabilization of dynamic systems described by vector differential equations

This paper considers the stability and constrained stabilization of dynamic systems described by second or higher order vector differential equations. Such systems arise in various applications including electromechanical systems, aerodynamics, structural analysis, robotics and vibration systems, in which the stabilization and improved performance play a crucial role. Due to the fact that the coefficient matrices of vector differential systems have special structures, it is of particular interest to maintain their structural properties while performing the design. The class of Metzlerian matrices is used as a constraint in the stabilization problem. Specifically, we provide a simple method to construct a stable feedback control law such that the closed-loop system matrix has the desired eigenvalues and maintains its original block companion structure with Metzlerian blocks.