This monograph introduces a newly developed robust-control design technique for a wide class of continuous-time dynamical systems called the "attractive ellipsoid method." Along with a coherent introduction to the proposed control design and related topics, the monograph studies nonlinear affine control systems in the presence of uncertainty and presents a constructive and easily implementable control strategy that guarantees certain stability properties. The authors discuss linear-style feedback control synthesis in the context of the above-mentioned systems. The development and physical implementation of high-performance robust-feedback controllers that work in the absence of complete information is addressed, with numerous examples to illustrate how to apply the attractive ellipsoid method to mechanical and electromechanical systems. While theorems are proved systematically, the emphasis is on understanding and applying the theory to real-world situations. Attractive Ellipsoids in Robust Control will appeal to undergraduate and graduate students with a background in modern systems theory as well as researchers in the fields of control engineering and applied mathematics.

This monograph introduces a newly developed robust-control design technique for a wide class of continuous-time dynamical systems called the "attractive ellipsoid method." Along with a coherent introduction to the proposed control design and related topics, the monograph studies nonlinear affine control systems in the presence of uncertainty and presents a constructive and easily implementable control strategy that guarantees certain stability properties. The authors discuss linear-style feedback control synthesis in the context of the above-mentioned systems. The development and physical implementation of high-performance robust-feedback controllers that work in the absence of complete information is addressed, with numerous examples to illustrate how to apply the attractive ellipsoid method to mechanical and electromechanical systems. While theorems are proved systematically, the emphasis is on understanding and applying the theory to real-world situations. Attractive Ellipsoids in Robust Control will appeal to undergraduate and graduate students with a background in modern systems theory as well as researchers in the fields of control engineering and applied mathematics.

This book is devoted to control of finite and infinite dimensional processes with continuous-time and discrete time control, focusing on suppression problems and new methods of adaptation applicable for systems with sliding motions only. Special mathematical methods are needed for all the listed control tasks. These methods are addressed in the initial chapters, with coverage of the definition of the multidimensional sliding modes, the derivation of the differential equations of those motions, and the existence conditions. Subsequent chapters discusses various areas of further research. The book reflects the consensus view of the authors regarding the current status of SMC theory. It is addressed to a broad spectrum of engineers and theoreticians working in diverse areas of control theory and applications. It is well suited for use in graduate and postgraduate courses in such university programs as Electrical Engineering, Control of Nonlinear Systems, and Mechanical Engineering.

This monograph presents some existing and new results on analysis and design of finite-time and fixed-time converging systems. Two main groups of approaches for analysis/synthesis of this kind of convergence, Lyapunov functions and the theory of homogeneous systems, are considered. The authors focus on the dynamics described by ordinary differential equations, time-delay models and partial differential equations. Some popular control and estimation algorithms, which possess accelerated converge rates, are also reviewed. Finally, the issues of discretization of finite-/fixed-time converging systems are discussed. Divided into 3 parts, this monograph provides the reader with a complete and accessible review of the topic. In the first part, the definitions of the different finite-/fixed-time stability properties are given together with their characterizations via the Lyapunov function approach. In the second part, several stabilization algorithms for linear and nonlinear systems are formalized, which are based on the implicit Lyapunov function approach. In the third part, the issues of discretization of finite-/fixed-time stable systems are discussed, with a special attention to the solutions obtained with the implicit Lyapunov function method. Finally, the accelerated converge concepts are presented for systems described by time-delay and partial differential equations. This monograph is an excellent introduction to the complex field of Finite-Time Stability Tools. It enables the reader to synthesize the important concepts and further their own research in the area.