ROBUST EIGENVALUE ASSIGNMENT FOR GENERALIZED SYSTEMS

In this paper we examine the problem of robust pole placement using state-feedback in generalized systems. We develop a robustness theory for the finite generalized spectrum of the system as a partial problem, and for the "infinite" pole placement problem as a second partial problem where perfect conditioning is always achievable. We also give bounds between the complete closed-loop robust eigenvalue problem and the two partial ones. The basic tool that is exploited in the presented theory, is the concept of chordal metric. In this paper we take advantage of this notion and present a compact theory for the robust eigenvalue assignment problem in generalized systems. The proposed theory is easy to implement, retrieves the results for the state-variable case as a special case, and takes advantage of well-known computational results.