Generalized pole placement via static output feedback: A methodology based on projections

Local Linear Convergence for Alternating and Averaged Nonconvex Projections

“…A good example is the set of matrices of some fixed rank: given a singular value decomposition of a matrix, projecting it onto this set is immediate. Furthermore, nonconvex alternating projection algorithms and analogous heuristics are quite popular in practice, in areas such as inverse eigenvalue problems [10,11], pole placement [35,51], information theory [48], low-order control design [23,24,36] and image processing [7,50]. Previous convergence results on nonconvex alternating projection algorithms have been uncommon, and have either focussed on a very special case (see for example [10,30]), or have been much weaker than for the convex case [14,48].…”

A Negative Imaginary Approach to Modeling and Control of a Collocated Structure

“…Also plotted in Fig. 12 is the simulated or predicted closed-loop re- sponse G (C l) y t ip w (jω), the FRF corresponding to (39). It can be observed that the predicted closed-loop response is reasonably close to the experimentally determined closed-loop response, except near the first resonance.…”

“…Therefore, the optimization problem (36) along with its associated LMI constraints can also be interpreted as a generalized pole placement problem via static output feedback, which is difficult to solve, [36]- [39]. A Bode plot of the pole optimized controller K IRC (s) obtained by minimizing (36) under the convex constraints, Γ > 0 and −D f > G(0) is plotted in Fig.…”

“…In Fig. 12, the predicted closed-loop response G (C l) y t ip w (jω), which is the FRF corresponding to (39), is plotted along with the model fitted for G y t ip w (jω) = G 11 (jω) plotted in Fig. 9.…”

On Application of the Ray-Shooting Method for LQR via Static-Output-Feedback

“…Assume that K (0) ∈ int (S α ) was found by the RS algorithm (see [16]) or by any other method (see [19][20][21]). Let h > 0 and let U (0) be a unit vector w.r.t.…”