Acceleration of finite-time stable homogeneous systems

Stabilization rates of power-integrator chains are easily regulated. It provides a framework for acceleration of uncertain multiple-input–multiple-output dynamic systems of known relative degrees (RDs). The desired rate of the output stabilization (sliding-mode control) is ensured for an uncertain system if its RD is known, and a rough approximation of the high-frequency gain matrix is available. The uniformly bounded convergence time (fixed-time stability) is obtained as a particular case. The control can be kept continuous everywhere except the sliding-mode set if the partial RDs are equal. Similarly, uncertain smooth systems of complete multiple-input–multiple-output RDs (ie, lacking zero dynamics) are stabilized by continuous control at their equilibria in finite time and are accelerated. Output-feedback controllers are constructed. Computer simulation demonstrates the efficiency of the proposed approach.