Towards Optimal Passive Feedback Control of LTI Systems under LQR Performance
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arXiv
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| Format: | Preprint |
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2026
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| author | Gießler, Armin Jané-Soneira, Pol Hohmann, Sören |
| author_facet | Gießler, Armin Jané-Soneira, Pol Hohmann, Sören |
| contents | We study state-feedback design for continuous-time LTI systems with a control input and an external input-output pair. Our objective is to determine feedback gains that render the closed-loop system (strictly) passive with respect to the external port while minimizing the standard LQR cost in the disturbance-free case. The resulting constrained optimization problem is intractable due to bilinear matrix inequalities. We analyze the set of passivating gains, showing it is unbounded, possibly nonconvex, path-connected, and contractible. We propose an indirect approach, in which the set of passivating feedback gains is inner-approximated by a compact, convex polytope. A projected gradient flow is employed to compute a gain within this polytope that minimizes the LQR cost. Numerical examples illustrate the effectiveness of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14854 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards Optimal Passive Feedback Control of LTI Systems under LQR Performance Gießler, Armin Jané-Soneira, Pol Hohmann, Sören Optimization and Control Systems and Control We study state-feedback design for continuous-time LTI systems with a control input and an external input-output pair. Our objective is to determine feedback gains that render the closed-loop system (strictly) passive with respect to the external port while minimizing the standard LQR cost in the disturbance-free case. The resulting constrained optimization problem is intractable due to bilinear matrix inequalities. We analyze the set of passivating gains, showing it is unbounded, possibly nonconvex, path-connected, and contractible. We propose an indirect approach, in which the set of passivating feedback gains is inner-approximated by a compact, convex polytope. A projected gradient flow is employed to compute a gain within this polytope that minimizes the LQR cost. Numerical examples illustrate the effectiveness of the method. |
| title | Towards Optimal Passive Feedback Control of LTI Systems under LQR Performance |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2604.14854 |