In some practices, not all state variables are available because of limited or noisy measurements. Thus, via output feedback, an observer is used to estimate the unmeasured states. To apply linear controllers to the pendulum-cart system, the Takagi-Sugeno fuzzy model is utilized by linearizing the system in more than one operating point. The effect of disturbances on tracking performance is reduced to the prescribed attenuation level by H∞ performance. The stability of the whole closed-loop system is investigated using the Lyapunov function. Sufficient conditions are derived in terms of a set of Linear Matrix Inequality (LMI) to obtain the controller and observer gain. Simulation results show that the proposed control method can make the system track the sinusoidal reference signal, maintain stability, and attenuate the effect of disturbances to less than the prescribed attenuation level measured by L2 gain. In the implementation process, an adjustment is needed to move the observer’s pole and speed up the observer’s responses.
Hierarchical Healthcare Referral System (HHRS) is implemented by National Insurance Providing Agency (BPJS) as part of the healthcare insurance policies. Patients who want to get health insurance in a hospital should get a referral from the community health center in which they are registered. Congestion of patients happens in certain hospital as there is no policy implemented to govern the referral system. In this paper, HHRS is modeled as a network of queuing system and is analyzed for its queue performances. Analysis of queuing network performances shows the influence patient preferences to buildup congestion of patients in hospitals. Referral is then controlled by means of dynamic routing with considering patient preferences. Estimation of arrival rate is done with hypercube queuing theory which concerns user preference. Simulation shows that patient preferences affect the arrival rate at each hospital, the application of dynamic routing can reduce the maximum utility and reduce the average waiting time, prioritization of patients improve dynamic routing performance on systems with a high workload.
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