Robust state feedback stabilisation of positive LTI systems with polytopic uncertainty

Abolpour, Roozbeh; Dehghani, Maryam; Sadabadi, Mahdieh S.

doi:10.1080/00207179.2022.2135025

International Journal of Control

2022

DOI: 10.1080/00207179.2022.2135025

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Robust state feedback stabilisation of positive LTI systems with polytopic uncertainty

Roozbeh Abolpour

Maryam Dehghani

Mahdieh S. Sadabadi

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2024

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Cited by 2 publications

References 31 publications

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Robust State‐Feedback Controller of Uncertain Systems Based on Non‐Monotonic Approach

El Fadili,

Boukili,

N'Diaye

et al. 2024

Adaptive Control & Signal

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In this article, new linear matrix inequality (LMI) conditions are proposed to guarantee robust stability of the closed‐loop of the linear time‐invariant one‐dimensional uncertain system by dealing with both continuous‐time (CT) and discrete‐time (DT) cases. These improved conditions for robust state feedback control combine the non‐monotonic approach and Finsler's technique. The benefit of the non‐monotonic approach returns to the utility of an arbitrary number of quadratic functions by considering the higher order derivatives of the vector field in the CT case (or the higher order differences of the vector field in the DT case). Finsler's technique aims to solve the closed‐loop stability problem in a larger parametric space. The strong points of the suggested LMI conditions are easy to program, eliminate the product between the state matrix and Lyapunov matrices, reduce the constraints by avoiding the decrease monotonically along trajectories for each quadratic Lyapunov function, guarantee the robust stability of the closed‐loop by using a state‐feedback gain. The simulation results show and confirm the effectiveness of these proposed conditions.

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Robust State‐Feedback Controller of Uncertain Systems Based on Non‐Monotonic Approach

El Fadili,

Boukili,

N'Diaye

et al. 2024

Adaptive Control & Signal

View full text Add to dashboard Cite

show abstract

Robust α -exponential estimate for polytopic uncertain positive discrete-time systems with bounded time-varying delay

Nguyen

2024

International Journal of Control

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Robust state feedback stabilisation of positive LTI systems with polytopic uncertainty

Cited by 2 publications

References 31 publications

Robust State‐Feedback Controller of Uncertain Systems Based on Non‐Monotonic Approach

Robust State‐Feedback Controller of Uncertain Systems Based on Non‐Monotonic Approach

Robust α -exponential estimate for polytopic uncertain positive discrete-time systems with bounded time-varying delay

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