Hybrid Stabilization of Linear Systems with Reverse Polytopic Input Constraints
Title | Hybrid Stabilization of Linear Systems with Reverse Polytopic Input Constraints |
Publication Type | Journal Article |
Year of Publication | 2017 |
Authors | Casau P., Sanfelice R.G, Silvestre C. |
Journal | IEEE Transactions on Automatic Control |
Volume | PP |
Issue | 99 |
Date Published | 02/02/2017 |
ISSN | 0018-9286 |
Other Numbers | Online ISSN: 1558-2523 |
Abstract | This paper addresses the problem of globally uniformly exponentially stabilizing a linear system to the origin by output feedback while avoiding a prescribed set of input values. We consider that the set of input values to avoid is given by the union of a finite number of closed polytopes that do not contain the origin and we refer to this restriction as a reverse polytopic input constraint. We show that the synthesis of the hybrid controller can be performed by solving a set of linear matrix inequalities for the full state feedback case, and by solving a set of bilinear matrix inequalities for the output feedback case. The resulting closed-loop hybrid system is shown to satisfy key conditions for well-posedness and robustness to small measurement noise. Furthermore, we apply the proposed hybrid controller to the stabilization of a single-input linear system subject to reverse polytopic constraints on the norm of the input. The behavior of the corresponding closed-loop hybrid system is validated by simulations. |
URL | http://ieeexplore.ieee.org/abstract/document/7845562/ |
DOI | 10.1109/TAC.2017.2665123 |