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基于非光滑的类二次型Lyapunov函数,对二阶滑模Super-twisting算法的有限时间收敛性进行了分析.当系统受常值干扰时,通过Lyapunov方程证明了该算法有限时间收敛,并给出了收敛时间的最优估计;当系统受时变干扰时,通过求解代数Riccati方程得出了一组保证该算法有限时间收敛的参数取值范围,并给出了收敛时间的估计值.仿真算例表明了理论分析的正确性.
Based on the non-smooth quasi-quadratic Lyapunov function, the finite-time convergence of the second-order sliding mode Super-twisting algorithm is analyzed. When the system is disturbed by a constant value, the Lyapunov equation is proved to be finite and the convergence of the algorithm is given The optimal estimation of convergence time is obtained. When the system is disturbed by time-varying, a set of parameter range is obtained by solving the algebraic Riccati equation to guarantee the convergence of the algorithm for a finite time, and the estimated convergence time is given. The example shows the correctness of the theoretical analysis.