## Quadratic Stabilization of Discrete-Time Uncertain Nonlinear Multi-Model Systems using Piecewise Affine State-Feedback (1998)

Venue: | International Journal of Control |

Citations: | 9 - 4 self |

### BibTeX

@ARTICLE{Slupphaug98quadraticstabilization,

author = {Olav Slupphaug and Bjarne A. Foss},

title = {Quadratic Stabilization of Discrete-Time Uncertain Nonlinear Multi-Model Systems using Piecewise Affine State-Feedback},

journal = {International Journal of Control},

year = {1998},

volume = {72},

pages = {686--701}

}

### OpenURL

### Abstract

In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI) feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of the state-space known as clusters the plant is assumed to be an element in a polytope which vertices (local models) are affine systems. In the clusters containing the origin in their closure, the local models are restricted to being linear systems. The clusters cover the region of interest in the state-space. An affine state-feedback is associated with each cluster. By utilizing the affinity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs) combined with a single nonconvex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed-loop. The feasibility problem is attacked by a branch-andbound based global approach. If the feasibility check is successful, the Liapunov matrix and the piecewise ...