Finite-Time Stability Tools for Control and Estimation

This survey 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 are considered: based on Lyapunov functions and the theory of homogeneous systems.The focus is put on the dynamics described by ordinary differential equations, time-delay models and partial differential equations.Some popular control and estimation algorithms, which posses accelerated converge rates, are reviewed.The issues of discretization of finite-/fixed-time converging systems are discussed.