Robust Control System Design Using Proportional Plus Partial Derivative State Feedback

Based on a general parametric eigenstructure assignment result proposed for descriptor linear systems via proportional plus partial derivative state feedback and a result for generalized eigenvalue sensitivity problem of matrix pairs, parametric representation of the closed-loop eigenvalue sensitivities to the perturbed elements in the open-loop system matrices is obtained. An effective algorithm for eigenvalue assignment with minimum sensitivity in descriptor linear systems via proportional plus partial derivative state feedback is then proposed. The algorithm does not contain ‘going back’ procedures, and allows the closed-loop eigenvalues to be conveniently optimized within desired regions. An example demonstrates its effectiveness and simplicity.