Stability and Performance Analysis on Self-dual Cones
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916537247465472 |
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| author | Vladu, Emil |
| author_facet | Vladu, Emil |
| contents | In this paper, we consider nonsymmetric solutions to certain Lyapunov and Riccati equations and inequalities with coefficient matrices corresponding to cone-preserving dynamical systems. Most results presented here appear to be novel even in the special case of positive systems. First, we provide a simple eigenvalue criterion for a Sylvester equation to admit a cone-preserving solution. For a single system preserving a self-dual cone, this reduces to stability. Further, we provide a set of conditions equivalent to testing a given H-infinity norm bound, as in the bounded real lemma. These feature the stability of a coefficient matrix similar to the Hamiltonian, a solution to two conic inequalities, and a stabilizing cone-preserving solution to a nonsymmetric Riccati equation. Finally, we show that the H-infinity norm is attained at zero frequency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12100 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability and Performance Analysis on Self-dual Cones Vladu, Emil Optimization and Control Systems and Control In this paper, we consider nonsymmetric solutions to certain Lyapunov and Riccati equations and inequalities with coefficient matrices corresponding to cone-preserving dynamical systems. Most results presented here appear to be novel even in the special case of positive systems. First, we provide a simple eigenvalue criterion for a Sylvester equation to admit a cone-preserving solution. For a single system preserving a self-dual cone, this reduces to stability. Further, we provide a set of conditions equivalent to testing a given H-infinity norm bound, as in the bounded real lemma. These feature the stability of a coefficient matrix similar to the Hamiltonian, a solution to two conic inequalities, and a stabilizing cone-preserving solution to a nonsymmetric Riccati equation. Finally, we show that the H-infinity norm is attained at zero frequency. |
| title | Stability and Performance Analysis on Self-dual Cones |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2411.12100 |