Observer design of positive quadratic systems

Okamoto, Yuji; Imura, Jun-ichi; Okada‐Hatakeyama, Mariko

doi:10.1109/ecc.2016.7810394

Cited by 6 publications

(3 citation statements)

References 19 publications

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“…For positive systems, in addition to minimizing this error, positive observers must also guarantee the nonnegativity of the state estimates [8,10,12]. This makes the positive observer design significantly more challenging [22], [2], [27]. .…”

Section: Introductionmentioning

confidence: 99%

Positive unknown inputs functional observers new design for positive linear systems

Ezzine,

Darouach,

Souley Ali

et al. 2024

Kybernetika

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This paper deals with the problem of designing positive functional observers for positive linear systems subject to unknown inputs. The order of the designed observer is equal to the dimension of the functional to be estimated. The designed functional observer is always nonnegative at any time and converges asymptotically to the real functional state vector. In fact, we propose a new positive reduced order observer for positive linear systems affected by unknown inputs. The proposed procedure is based on the positivity of an augmented system composed of dynamics of both considered system and proposed observer and also, on the unbiasedness of the estimation error by the resolution of Sylvester equation. Then existence conditions of such observers are formulated in terms of linear programming (LP) problem, where we use the Perron-Frobenius theorem applied to Metzler matrices. An algorithm that summarizes the different steps of the proposed positive functional observer design is given. Finally, numerical example and simulation results are given to illustrate the effectiveness of the proposed design method.

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Section: Introductionmentioning

confidence: 99%

Positive unknown inputs functional observers new design for positive linear systems

Ezzine,

Darouach,

Souley Ali

et al. 2024

Kybernetika

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“…Recently, an impulsive positive observer has been developed for continuous-time positive linear systems (Xiao et al, 2017). Positive observers have been extended for other types of positive systems such as switched systems (Wang et al, 2016), quadratic systems (Okamoto et al, 2016), time-delay systems (Trinh et al, 2017), linear impulsive delayed systems (Hu et al, 2017), and positive 2D discrete-time systems (Shen and Wang, 2017). Moreover, there are few articles presenting observers for uncertain positive systems (Chen and Lam, 2014; Chen et al, 2014; Li and Lam, 2012), and also in the presence of unknown input or disturbances (Shafai et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

Motahhari

Shafiei

2020

Transactions of the Institute of Measurement and Control

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This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

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“…For this reason, in addition to minimising the estimate error, positive observers must also ensure the state estimates are always non‐negative. This makes the positive observer design significantly more challenging [11–15]. In recent years, significant advances have been made in the design of observers for positive systems.…”

Section: Introductionmentioning

confidence: 99%