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The purpose of this paper is to investigate the design method of partial observer canonical form (POCF), which is one of the important research tools for industrial plants.

Motivated by the two-steps method proposed in Xu et al. (2020), this paper extends this method to the case of Multi-Input Multi-Output (MIMO) nonlinear system. It decomposes the original system into two subsystems by observable decomposition theorem first and then transforms the observable subsystem into OCF. Furthermore, the necessary and sufficient conditions for the existing of POCF are proved.

The proposed method has a wide range of applications including completely observable nonlinear system, noncompletely observable nonlinear system, autonomous nonlinear system and forced nonlinear system. Besides, comparing to the existing results (Saadi et al., 2016), the method requires less verified conditions.

The new method concerning design POCF has better plants compatibility and less validation conditions.

The present study is undertaken in the region of Guelma that is located in North-Eastern Algeria. Guelma’s agricultural plain is irrigated from the Seybouse ephemeral river (wadi). The latter collects the entire domestic and industrial wastewaters of the region that are discharged without prior treatment. Hence, the organic and biological or what so ever contributions to the wadi are capable of initiating a significant degradation of its waters’ quality and challenging their use for irrigation. The paper aims to discuss these issues.

The interpretation of the results of three sampling campaigns for chemical and bacteriological analyzes was carried out in terms of the indices’ method (organic pollution index (OPI) and microbiological quality index (MQI)). The results were statistically assessed through the use of the principal component analysis (PCA). The OPI was calculated according to the method of Leclercq and Maquet (1987) whose principle is to classify the contents for the polluting elements into 5 classes each class corresponding to a given range for the considered parameter, and then to calculate the overall average class number for each sample. The MQI depends on the water concentrations in: the total coliforms, the fecal coliforms, and fecal streptococci. One defines five classes of concentrations for each of these parameters. The MQI is again the overall mean of the numbers for the classes for every parameter.

The OPI reflects a moderate pollution for most sampling stations. The PCA indicates that the variables controlling salinity are mainly Cl⁻, Na⁺ and SO₄²⁻. In August 2016, El-Fedjoudj pumping station shows a very strong fecal contamination. According to the recommendations of World Health Organization (1989), waters from wadi Seybouse cannot be used for the irrigation of vegetable crops if they were to be consumed raw.

This study has an environment impact as it reveals the need to protect surface waters used for irrigation and therefore protect consumers of raw vegetables that are to be consumed uncooked.