Stabilization of large-scale systems by reduced order controllers

It is demonstrated that a reduced-order controller that uses the state of a reduced-order model of the original system for feedback purposes can stabilize the original system if a certain condition is satisfied. In the approach to deriving the condition, it is assumed that the nondominant part of the original system may be linearly approximated by the dominant part. The approach taken for the derivation of these conditions is based on the identification and partition of the slow and fast parts of the original system. A Lyapunov function for the original system is formed as a linear combination of the states of the original system which are associated with the slow and fast parts. The fast mode of the system is then approximated in terms of the slower one. As a result, a modified Lyapunov function is obtained from which the condition for global stability is derived. An example is given to illustrate the approach used