This study deals with constant-gain adaptive observers for nonlinear systems, for which relatively few solutions are available for some particular cases. We introduce an asymptotic observer of constant gain for nonlinear systems that have linear input. This allows the observer design to be formulated within the linear matrix inequality paradigm provided that a strictly positive real condition between the input disturbance and the output is fulfilled. The proposed observer is then applied to a large class of nonlinear chemostat dynamical systems that are widely used in the fermentation process, cell cultures, medicine, etc. In fact, under standard practical assumptions, the necessary change of the chemostat state coordinates exists, allowing use of the constant-gain observer. Finally, the developed theory is illustrated by estimating pollutant concentration in a Spirulina maxima wastewater treatment facility.

这项研究涉及非线性系统的恒定增益自适应观测器，在某些特殊情况下，相对可用的解决方案相对较少。对于具有线性输入的非线性系统，我们引入了恒定增益的渐近观测器。只要满足输入干扰和输出之间的严格正实条件，就可以在线性矩阵不等式范式内制定观察者设计。然后将拟议的观察者应用于一类广泛用于发酵过程，细胞培养，医学等方面的非线性化学恒温动力学系统。实际上，在标准的实际假设下，化学恒温状态的坐标存在必要的变化，使用恒定增益观察器。最后，螺旋藻最大废水处理设施。