Essence of Fractional Order Calculus, Physical Interpretation and Applications -- Solution, Stability and Realization of Fractional Order Differential Equation -- Sliding Mode Control of Fractional Order Systems -- Finite Time Stabilization of Fractional Order Systems -- A Soft Variable Structure Control of Fractional Order Systems -- Robust Cooperative Control of Fractional-Order Multiple Agents -- Discrete Sliding Mode Control of Fractional Order systems -- Disturbance Observer based Robust Control for Fractional Order Systems -- Contraction Analysis by Integer Order and Fractional Order Infinitesimal Variations.

In the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis. This monograph is based on the authors’ work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the third chapter are written in tutorial fashion, presenting all the basic concepts of fractional order system and a brief overview of sliding mode control of fractional order systems. The other parts contain deal with robust finite time stability of fractional order systems, integral sliding mode control of fractional order systems, co-operative control of multi-agent systems modeled as fractional differential equation, robust stabilization of discrete fractional order systems, high performance control using soft variable structure control and contraction analysis by integer and fractional order infinitesimal variations.