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讨论一类含有限能量未知扰动的线性Markov跳变系统的有限时间镇定问题.针对连续系统和离散系统两种情况,利用构造的Lyapunov-Krasovskii函数,并结合线性矩阵不等式方法,分别证明并给出了跳变系统有限时间镇定控制器有解的充分条件.采用该方法设计的镇定控制器可使连续系统和离散系统对所有满足条件的未知扰动是有限时间有界和有限时间镇定的.最后通过数值示例表明了该设计方法的有效性.
In this paper, we discuss the finite-time stabilization problem for a class of linear Markov transition systems with unknown disturbance of finite energy. For the two cases of continuous systems and discrete systems, the constructed Lyapunov-Krasovskii functions are combined with the linear matrix inequalities to prove and give respectively The sufficient conditions for the existence of solutions for the stabilization of a transition system with finite time are obtained.The stabilization controller designed by this method can make the continuous system and the discrete system be finite finite time bounded and finitely stable for all unknown disturbances satisfying the conditions.Finally, Numerical examples show the effectiveness of this design method.