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Acceleration of finite‐time stable homogeneous systems
Author(s) -
Dvir Y.,
Levant A.,
Efimov D.,
Polyakov A.,
Perruquetti W.
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3984
Subject(s) - control theory (sociology) , acceleration , bounded function , convergence (economics) , mathematics , integrator , sliding mode control , stability (learning theory) , computer science , control (management) , nonlinear system , mathematical analysis , physics , computer network , bandwidth (computing) , classical mechanics , quantum mechanics , artificial intelligence , machine learning , economics , economic growth
Summary 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.