This paper considers  state feedback with decentralized structure for interconnected systems. The connection between subsystems is described by a directed graph. To design a decentralized  controller, we use the information from its own subsystem and other subsystems based on the interconnection. Decentralized controller is defined as a solution of bilinear matrix inequality (BMI) problem, which is then solved by using the homotopy approach. Two numerical examples are performed to show validity of the design procedure

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Saat ini pandemi Covid-19 telah menyebar ke seluruh dunia, tidak terkecuali Indonesia. Dalam pemodelan matematika, penyebaran Covid-19 dapat digambarkan melalui model matematika epidemiologi SIRD (Susceptible, Infected, Recover, Death). Pertama model non-linier SIRD didiskritkan dan selanjutnya dilakukan prediksi puncak penyebaran Covid-19 dengan menggunakan metode Extended Kalman Filter (EKF). Dengan data aktual Infected, Recover, dan Death yang merupakan data harian, modifikasi EKF dapat memprediksi puncak infeksi Covid-19 untuk satu bulan kedepan. Simulasi dilakukan dengan 3 macam pembatasan pergerakkan pada masyarakat yaitu : tanpa adanya pembatasan (100%), 75%, dan 50% pergerakkan. Hasil prediksi dengan modifikasi EKF menunjukkan dengan dilakukan pembatasan pergerakkan 50% pada masyarakat di Indonesia dan Jawa Timur dapat mempercepat terjadinya puncak infeksi dengan jumlah individu terinfeksi lebih sedikit.

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This paper will discuss the estimation of the multi-robot position. It may be difficult for all sensors to submit their observations due to communication constraints on the multi-robot system. Thus, in this paper, we will estimate the position of each robot with limited communication between robots using decentralized estimation. Since the multi-robot system is non-linear, the extended Kalman filter is used as an estimation method. The combination of decentralized estimation and extended Kalman filter is called a decentralized extended Kalman filter. In the multi-robot system, each robot is represented as a node that makes its prediction. Assumed that some of the nodes will interact with their closest neighbors, so the measurement information will be transferred. Based on simulation results, the decentralized extended Kalman filter algorithm runs well for estimation in a multi-robot position.