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PID Output-Feedback Control and Filtering for Positive Roesser System

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Abstract

This paper considers the output-feedback-based proportional–integral–derivative (PID) control and filtering problems for the discrete-discrete Roesser system with disturbances. A PID output-feedback controller, where the integral loop is with fixed time-window, is first constructed for the two-dimensional system. By means of co-positive Lyapunov function approach, sufficient conditions are proposed to ensure that the resulting closed-loop system is positive, exponentially stable and has an \(l_1\)-gain bound \(\gamma \). In addition, the gains of desired PID controller are then appropriately parameterized by solutions to certain linear programming problems. An illustrated example is provided to show effectiveness of the PID controller designed.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work was supported in part by the National Key Research and Development Program of China under Grant 2018AAA0100202, in part by the Research Foundation of Jinling Institute of Technology under Grant Jit-b-202047, and in part by the Fundamental Research Funds for the Central Universities under Grant 2242023K40010.

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 210096, China

    Na Zhang & Jinling Liang

  2. College of Science, Jinling Institute of Technology, Nanjing, 211169, China

    Dehao Li

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  1. Na Zhang
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  2. Jinling Liang
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Correspondence to Jinling Liang.

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Zhang, N., Liang, J. & Li, D. PID Output-Feedback Control and Filtering for Positive Roesser System. Circuits Syst Signal Process 43, 152–171 (2024). https://doi.org/10.1007/s00034-023-02484-2

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