Robust pole assignment in descriptor linear systems via state feedback

Robust Eigenvalue Assignment in Descriptor Systems via Output Feedback

“…Since the closed-loop finite eigenvalues are also included in the design parameters and are optimized within desired regions in the complex plane, this algorithm can usually give a closed-loop system with better robustness. Moreover, because the completeness of the eigenstructure assignment approach used, the optimality of the solution to the robust pole assignment problem obtained through Algorithm RPA is totally dependent on the solution to the optimization problem (20) (or (28) and (29)). However, since the optimization (20) or (28) is generally a non-convex nonlinear programming, it is very difficult to produce an algorithm for solving this optimization with theoretical guarantee of global optimality.…”

“…Particularly, when the observation matrix C reduces to the identity matrix, the result becomes the one for robust pole assignment in descriptor linear systems via state feedback proposed in [28]; and when the open-loop system (1) becomes a normal linear system, the proposed result becomes the one in [21]. Other very closely related works are [26], which treats robust pole assignment in descriptor linear systems via proportional plus derivative state feedback, and [8], which treats robust pole assignment in normal linear systems via dynamical output feedback.…”

Robust Eigenvalue Assignment in Descriptor Systems via Output Feedback

“…Moreover, because the completeness of the eigenstructure assignment approach used, the optimality of the solution to the robust pole assignment problem obtained through Algorithm RPA is totally dependent on the solution to the optimization problem (20) (or (28) and (29)). Moreover, because the completeness of the eigenstructure assignment approach used, the optimality of the solution to the robust pole assignment problem obtained through Algorithm RPA is totally dependent on the solution to the optimization problem (20) (or (28) and (29)).…”

“…Particularly, when the observation matrix C reduces to the identity matrix, the result becomes the one for robust pole assignment in descriptor linear systems via state feedback proposed in [28]; and when the open-loop system (1) becomes a normal linear system, the proposed result becomes the one in [21]. Particularly, when the observation matrix C reduces to the identity matrix, the result becomes the one for robust pole assignment in descriptor linear systems via state feedback proposed in [28]; and when the open-loop system (1) becomes a normal linear system, the proposed result becomes the one in [21].…”

The solution to the matrix equationAV + BW = EVJ + R

“…It follows from the proof of Lemma 2.2, that the unimodular matrix Q(s) can be easily obtained based on the Smith form reduction (2.8), while the Smith form reduction (2.8) can be easily realized by manually using some simple elementary matrix transformations for relatively lower-order cases. This offers a great advantage in certain control applications, where the closed-loop eigenvalues can be regarded undetermined and used as a part of the design parameters (see, e.g., [12][13][14]). REMARK 3.3.…”