Reduced Order Dynamics Assignment for State Feedback Control and State Estimation Design by SVD of the Projections

This work is concerned with the problem of designing stable invariant subspaces for the construction of discontinuity surfaces of variable structure control systems (VSCS). A new method of analyzing and designing the closed loop systems, such as the model following control systems and VSC systems with sliding mode, having desirable behavior in tracking or regulation is developed in this paper. The study has been motivated by the observation that a basic operator associated with the assignment of dynamics in feedback control system qualifies as a projector. Projector theory provides a neat method for analysis and design of VSCS to construct the sliding manifolds in class of differentiate manifolds. Reducibility and invariance properties of projections make them very attractive to decompose a dynamic system into lower order two subsystems decoupled from each other, so we get deep insight into problems in analysis and design tasks of control systems and more information about dynamics incorporated with "modes" and eigenvectors represent intrinsic properties of dynamical systems