A successive projection method
Mathematical Programming: Series A and B
Method of successive projections for finding a common point of sets in metric spaces
Journal of Optimization Theory and Applications
Automatica (Journal of IFAC)
Parametrization of all stabilizing controllers via quadratic Lyapunov functions
Journal of Optimization Theory and Applications
A primal-dual potential reduction method for problems involving matrix inequalities
Mathematical Programming: Series A and B
Technical communique: Structurally constrained H2 and H∞ control: A rank-constrained LMI approach
Automatica (Journal of IFAC)
Survey paper: Static output feedback-A survey
Automatica (Journal of IFAC)
A Newton-like method for solving rank constrained linear matrix inequalities
Automatica (Journal of IFAC)
Generalized pole placement via static output feedback: A methodology based on projections
Automatica (Journal of IFAC)
Technical Communique: Static Output Feedback Stabilization: An ILMI Approach
Automatica (Journal of IFAC)
Brief Decentralized H∞ controller design: a matrix inequality approach using a homotopy method
Automatica (Journal of IFAC)
Robust output-feedback controller design via local BMI optimization
Automatica (Journal of IFAC)
Reduced-order controllers for the H∞ control problem with unstable invariant zeros
Automatica (Journal of IFAC)
Probabilistic design of LPV control systems
Automatica (Journal of IFAC)
Hi-index | 22.16 |
Computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities (LMIs). In particular, we concentrate on the stabilization and the suboptimal H"~ output feedback control design problems. These problems can be described by a pair of LMIs and an additional coupling condition. This coupling condition is convex for the full-order control design problem, but convexity is lost for the control problem of order strictly less than the plant order. We formulate these problems as feasibility problems with matrix constraint sets of simple geometry, and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets. Full-order and low-order controllers are designed using alternating projection methods. For the full-order controller case, global convergence of the alternating projection methods to a feasible solution is guaranteed. However, for the low-order control case, only local convergence is guaranteed. An example is provided to illustrate the use of these methods for the full-order and the low-order controller design.