7. Conclusion

This tutorial was devoted to a brief introduction to the topic of finite/fixed-time stabilization and estimation in dynamical systems. Starting from motivating examples, the formal definitions of various stability and robust stability concepts were given with their characterizations using the Lyapunov function method establishing the base for detecting and imposing these convergence rates in different practical scenarios of analysis or control design. The theory of homogeneous systems was presented since it constitutes a beautiful and useful framework for analysis and design of dynamical systems possessing accelerated convergence rates being robust to various perturbations. Examples of stabilizing control and state estimation algorithms were given for linear systems. Application of the implicit Lyapunov function method allowed us to formulate the tuning rules using the computationally tractable...