Linear systems controlled by stabilized constraint relations

The author considers the task of designing a control law that forces selected state variables of a linear system to satisfy prescribed algebraic constraint relations and simultaneously guarantees pole placement of the closed-loop system. This task leads to a system representation in semistate form. On the assumption that the system is regular singular, the task is solved in the following steps. The constrained relations are stabilized with prescribed stabilization eigenvalues. Feedback and feedforward controllers that force the control plant to satisfy the constraint relations according to the stabilization dynamics are derived. Implementation conditions of the constraint control laws are derived. The remainder eigenvalues of the constraint control plant that are not fixed by the constraint stabilization are placed by an additional control loop. A constraint separation principle that guarantees an independent choice of the eigenvalues associated with the constraint variables and of those eigenvalues that are associated with the unconstraint variables is proved. The invariance of the stabilized constraint relation under the second control loop is also proved