The book illustrates the theoretical results of fractional derivatives via applications in signals and systems, covering continuous and discrete derivatives, and the corresponding linear systems. Both time and frequency analysis are presented. Some advanced topics are included like derivatives of stochastic processes. It is an essential reference for researchers in mathematics, physics, and engineering.

The book illustrates the theoretical results of fractional derivatives via applications in signals and systems, covering continuous and discrete derivatives, and the corresponding linear systems. Both time and frequency analysis are presented. Some advanced topics are included like derivatives of stochastic processes. It is an essential reference for researchers in mathematics, physics, and engineering.

This book presents a collection of exercises on dynamical systems, modelling and control. Each topic covered includes a summary of the theoretical background, problems with solutions, and further exercises. Topics covered include: block diagram algebra and system transfer functions; mathematical models; analysis of continuous systems in the time domain; root locus analysis; frequency domain analysis; PID controller synthesis; state space analysis of continuous systems; controller synthesis by pole placement; discrete time systems and the Z transform; analysis of non-linear systems with the describing function method; analysis of nonlinear systems with the phase plane method; and fractional order systems and controllers. Based on tried-and-tested problems and solutions that the authors use in teaching over 500 students each year, this book is essential reading for advanced students with courses in modelling and control in engineering, applied mathematics, biomathematics and physics.

Fractional control techniques provide an effective way to control dynamic behaviors, using fractional differential equations. This can include the control of fractional plants, the control of a plant using a fractional controller, or the control of a plant so that the controlled system will have a fractional behaviour to achieve a performance that would otherwise be hard to come by. "An Introduction to Fractional Control" outlines the theory, techniques and applications of fractional control. The theoretical background covers fractional calculus with real, complex and variable orders, fractional transfer functions, fractional identification and pseudostatespace representations, while the control systems explored include: fractional lead control, fractional lag control, first, second and third generation Crone control, fractional PID, PI and PD control, fractional sliding mode control, logarithmic phase Crone control, fractional reset control, fractional H2 and H8 control, fractional predictive control, trajectory planning and fractional timevarying control. Each chapter contains solved examples, where the subject addressed is either expanded or applied to concrete cases, and references for further reading. Common definitions and proofs are included, along with a bibliography, and a discussion of how MATLAB can be used to assist in the design and implementation of fractional control. This is an essential guide for researchers and advanced students of control engineering in academia and industry.