Two types of nonlinear control algorithms are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.

This study focuses on the design of fixed‐time consensus for first‐order multi‐agent systems with unknown inherent non‐linear dynamics. A distributed control protocol, based on local information, is proposed to ensure the convergence of the tracking errors in finite time. Some conditions are derived to select the controller gains in order to obtain a prescribed convergence time regardless of the initial conditions. Simulations are performed to validate the theoretical results.

A method of a Lyapunov functions design based on resolving of the first-order partial differential equation of a special type is presented. A successful resolution of this equation guaranties a finite-time convergence for the corresponding dynamics given by an ordinary differential equation with a discontinuous right-hand side. It is also provides an analytical formula for an upper bound of the corresponding reaching time. The suggested method is applied to the problem of a stability analysis and a reaching time estimation of the, so-called, ldquosuper-twistingrdquo controller. The estimation accuracy is confirmed by numerical example.