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.