Robust stability and performance analysis of positive systems using linear programming

Babazadeh, Maryam; Nobakhti, Amin

doi:10.1109/med.2016.7535955

Cited by 3 publications

(2 citation statements)

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“…Three controller gain matrices need to be designed. From (7), the closed-loop system refers to the delay. How to reach the positivity and stability of the system is difficult to be handled.…”

Section: Resultsmentioning

confidence: 99%

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Linear programming‐based proportional‐integral‐derivative control of positive systems

Zhou

Zhang

Jia

et al. 2023

IET Control Theory & Appl

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This paper investigates the proportional‐integral‐derivative (PID) control of positive systems in the discrete‐time case. First, a tuning parameter is introduced to construct the proportional‐integral‐derivative control framework of positive systems. The proportional‐integral‐derivative control problem is thus transformed into the control synthesis of positive systems with time‐delay. By virtue of a matrix decomposition approach, the gain matrices of proportional‐integral‐derivative controller are designed. Using co‐positive Lyapunov functions and linear programming, the positivity and stability of positive systems are achieved under the designed proportional‐integral‐derivative controller. Then, the proportional‐integral‐derivative control of positive systems with reference signal is solved. The main contribution of this paper lies in that linear programming associated to the matrix decomposition approach is first presented to handle the proportional‐integral‐derivative control of positive systems. Finally, two illustrative examples are provided to verify the effectiveness of the proposed design.

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Section: Resultsmentioning

confidence: 99%

“…These applications also motivate the theoretical research of positive systems. The literature [7] investigated the robust stability of positive systems with structured uncertainties by virtue of linear programming. In [8], the controllability and reachability of two‐dimensional positive systems were discussed by means of graph theory.…”

Section: Introductionmentioning

confidence: 99%