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"The theory of linear functional observers, which is the subject of this book, is increasingly becoming a popular researched topic because of the many advantages it presents in state observation and control system design. This book presents recent information on the current state of the art research in this field. This book will serve as a useful reference to researchers in this area of research to understand the fundamental concepts relevant to the theory of functional observers and to gather most recent advancements in the field. "

"Saturated switching systems treats the problem of actuator saturation, inherent in all dynamical systems by using two approaches: positive invariance in which the controller is designed to work within a region of non-saturating linear behaviour and saturation technique which allows saturation but guarantees asymptotic stability. The results obtained are extended from the linear systems in which they were first developed to switching systems with uncertainties, 2D switching systems, switching systems with Markovian jumping and switching systems of the Takagi-Sugeno type. The text represents a thoroughly referenced distillation of results obtained in this field during the last decade. The selected tool for analysis and design of stabilizing controllers is based on multiple Lyapunov functions and linear matrix inequalities. All the results are illustrated with numerical examples and figures many of them being modelled using MATLAB®. "

"The book includes a theory for flow barriers and passability to boundaries in discontinuous dynamical systems that will completely change traditional concepts and ideas in the field of dynamical systems. Edge dynamics and switching complexity of flows in discontinuous dynamical systems are explored in the book and provide the mathematical basis for developing the attractive network channels in dynamical systems. The theory of bouncing flows to boundaries, edges and vertexes in discontinuous dynamical systems with multi-valued vector fields is described in the book as a “billiard” theory of dynamical system networks. The theory of dynamical system interactions in discontinued dynamical systems can be used as a general principle in dynamical system networks, which is applied to dynamical system synchronization.　"

"Sistem multi-agent dikembangkan untuk meningkatkan efisiensi kerja dan untuk mengoptimalkan kemampuan beberapa agent yang terdapat dalam satu kesatuan. Ada berbagai masalah yang berkaitan dengan sistem multi-agent, salah satunya adalah masalah konsensus, yang berkaitan dengan hubungan komunikasi antar agent. Tanpa adanya konsensus maka agents tidak dapat mencapai kesepakatan untuk bekerja sama dalam melakukan tugas yang diberikan.Pada skripsi ini, diajukan dua protokol pengendali berbasis observer terdistribusi untuk sistem leader-following multi-agent waktu diskrit. Pada kasus yang pertama, observer terdistribusi tersebut digunakan untuk mengestimasi keadaan leader dan untuk yang kedua, observer terdistribusi digunakan untuk mengestimasi kesalahan pelacakan berdasarkan keluaran relatif dari neighboring agent. Protokol pengendali konsensus ini didesain berdasarkan teori kendali optimal, yaitu persamaan aljabar Riccati. Matriks gain yang digunakan pada sinyal kendali diperoleh dari penyelesaian persamaan aljabar Riccati waktu diskrit. Sementara untuk observer, matriks gain yang digunakan diperoleh dari penyelesaian persamaan aljabar Riccati waktu diskrit yang dimodifikasi.Kedua protokol pengendali berbasis observer terdistribusi diuji coba pada topologi undirected graph yang tetap dan berubah. Hasil uji coba simulasi menunjukkan bahwa keadaan follower agent menunjukkan konvergensi menuju keadaan leader agent, yang artinya masalah konsensus tercapai melalui penggunaan kedua protokol pengendali yang diajukan.

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Multi agent system is developed to improve work efficiency and to optimize the capabilities of multiple agents in a single entity. There are various problems related to multi agent system, one of which is consensus problem, which is related to communication between agents. Without consensus, the agents can not reach agreement to cooperate in performing the given task.In this thesis, two distributed based control protocols are proposed for discrete time leader following multi agent system. For the first case, the distributed observer is used to estimate the leader 39 s state and for the second, the distributed observer is used to estimate the tracking error based on the relative output of the neighboring agent.

This consensus control protocol is designed based on the optimal control theory, which is the algebraic Riccati equation. The gain matrix used in the control signal is obtained from solving the discrete time algebraic Riccati equations. As for the observer, the gain matrix is obtained from solving the modified discrete time algebraic Riccati equation.Both distributed observer based control protocols are tested on fixed and switching topology of undirected graphs. The simulation results show that the follower rsquo s state converge toward the leader rsquo s state, which means the consensus problem is achieved through the use of both proposed control protocols."

"Regularity and complexity in dynamical systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems."