Control of Discrete-Time Linear Systems with Charge-Balanced Inputs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914187592073216 |
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| author | Qin, Yuzhen Liu, Zonglin van Gerven, Marcel |
| author_facet | Qin, Yuzhen Liu, Zonglin van Gerven, Marcel |
| contents | Electrical brain stimulation relies on externally applied currents to modulate neural activity, but safety constraints require each stimulation cycle to be charge-balanced, enforcing a zero net injected charge. However, how such charge-balanced stimulation works remains poorly understood. This paper investigates the ability of charge-balanced inputs to steer state trajectories in discrete-time linear systems. Motivated by both open-loop and adaptive neurostimulation protocols, we study two practically relevant input structures: periodic (repetitive) charge-balanced inputs and non-repetitive charge-balanced inputs. For each case, we derive novel reachability and controllability conditions. The theoretical results are further validated through numerical demonstrations of minimum-energy control input design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Control of Discrete-Time Linear Systems with Charge-Balanced Inputs Qin, Yuzhen Liu, Zonglin van Gerven, Marcel Systems and Control Optimization and Control Electrical brain stimulation relies on externally applied currents to modulate neural activity, but safety constraints require each stimulation cycle to be charge-balanced, enforcing a zero net injected charge. However, how such charge-balanced stimulation works remains poorly understood. This paper investigates the ability of charge-balanced inputs to steer state trajectories in discrete-time linear systems. Motivated by both open-loop and adaptive neurostimulation protocols, we study two practically relevant input structures: periodic (repetitive) charge-balanced inputs and non-repetitive charge-balanced inputs. For each case, we derive novel reachability and controllability conditions. The theoretical results are further validated through numerical demonstrations of minimum-energy control input design. |
| title | Control of Discrete-Time Linear Systems with Charge-Balanced Inputs |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2512.07506 |