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arXiv · 1608.00426

The $\epsilon$-capacity of a gain matrix and tolerable disturbances: Discrete-time perturbed linear systems

O Zakary·M Rachik
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Abstract

Discrete-time linear systems with perturbed initial state are considered. A disturbance that infects the initial state is said to be $\epsilon$-tolerable if the corresponding output signal is relatively insensitive to their effects. In this paper, we will define a new set that characterize each gain matrix K and the associated feedback control law ui=Kxi, this set will be called the $\epsilon$-capacity of the gain matrix K. The set of all possible gain matrix that makes the system insensitive to all disturbances is noted $\Phi\cdot$. The characterization of $\Phi\cdot$ is investigated, and we propose an algorithmic approach that allows to determine if a control law is belongs to $\Phi\cdot$ or not. Numerical simulations are given.

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O Zakary, M Rachik. 2016-07-27. The $\epsilon$-capacity of a gain matrix and tolerable disturbances: Discrete-time perturbed linear systems. https://doi.org/10.9790/5728-11345262

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