Tuberculosis (TB) is a contagious disease which can easily be disseminated in a society. A five state Susceptible, exposed, infected, recovered and resistant (SEIRs) epidemiological mathematical model of TB has been considered along with two non-linear controllers: State Feedback (SFB) and Synergetic controllers have been designed for the control and prevention of the TB in a population. Using the proposed controllers, the infected individuals have been reduced/controlled via treatment, and susceptible individuals have been prevented from the disease via vaccination. A mathematical analysis has been carried out to prove the asymptotic stability of proposed controllers by invoking the Lyapunov control theory. Simulation results using MATLAB/Simulink manifest that the non-linear controllers show fast convergence of the system states to their respective desired levels. Comparison shows that proposed SFB controller performs better than Synergetic controller in terms of convergence time, steady state error and oscillations.

中文翻译：

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感染人群中结核病的状态反馈和协同控制器。

结核病是一种传染性疾病，很容易在社会中传播。考虑了五个状态的结核病易感，暴露，感染，恢复和耐药（SEIR）流行病学数学模型，以及两个非线性控制器：状态反馈（SFB）和协同控制器设计用于控制和预防结核病在人口中。使用所提出的控制器，已通过治疗减少/控制了受感染的个体，并已通过接种疫苗预防了易感者的疾病。通过调用Lyapunov控制理论进行了数学分析，以证明所提出控制器的渐近稳定性。使用MATLAB / Simulink进行的仿真结果表明，非线性控制器显示出系统状态快速收敛至其所需水平的收敛。比较表明，所提出的SFB控制器在收敛时间，稳态误差和振荡方面均优于Synergetic控制器。