Multivariable Generalized Super-Twisting Algorithm Robust Control of Linear Time-Invariant Systems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910845800284160 |
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| author | Geromel, J. C. Nunes, E. V. L. Hsu, L. |
| author_facet | Geromel, J. C. Nunes, E. V. L. Hsu, L. |
| contents | This paper presents a novel procedure for robust control design of linear time-invariant systems using a Multivariable Generalized Super-Twisting Algorithm (MGSTA). The proposed approach addresses robust stability and performance conditions, considering convex bounded parameter uncertainty in all matrices of the plant state-space realization and Lipschitz exogenous disturbances. The primary characteristic of the closed-loop system, sliding mode finite-time convergence, is thoroughly examined and evaluated. The design conditions, obtained through the proposal of a novel max-type non-differentiable piecewise-continuous Lyapunov function are formulated as Linear Matrix Inequalities (LMIs), which can be efficiently solved using existing computational tools. A fault-tolerant MGSTA control is designed for a mechanical system with three degrees of freedom, illustrating the efficacy of the proposed LMI approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18868 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multivariable Generalized Super-Twisting Algorithm Robust Control of Linear Time-Invariant Systems Geromel, J. C. Nunes, E. V. L. Hsu, L. Systems and Control This paper presents a novel procedure for robust control design of linear time-invariant systems using a Multivariable Generalized Super-Twisting Algorithm (MGSTA). The proposed approach addresses robust stability and performance conditions, considering convex bounded parameter uncertainty in all matrices of the plant state-space realization and Lipschitz exogenous disturbances. The primary characteristic of the closed-loop system, sliding mode finite-time convergence, is thoroughly examined and evaluated. The design conditions, obtained through the proposal of a novel max-type non-differentiable piecewise-continuous Lyapunov function are formulated as Linear Matrix Inequalities (LMIs), which can be efficiently solved using existing computational tools. A fault-tolerant MGSTA control is designed for a mechanical system with three degrees of freedom, illustrating the efficacy of the proposed LMI approach. |
| title | Multivariable Generalized Super-Twisting Algorithm Robust Control of Linear Time-Invariant Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2502.18868 |