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应用微分博弈理论研究了噪声依赖于状态x(t)、控制u(t)和干扰v(t)的Ito型线性马尔可夫跳变系统H∞鲁棒控制设计问题.首先将系统的控制变量u(t)视为博弈的一方,随机性干扰v(t)视为博弈的另一方,从而把H∞鲁棒控制问题转化为一个二人零和微分博弈问题,然后通过分析此微分博弈问题得到了H∞鲁棒控制存在的条件等价于相应的矩阵Riccati代数方程存在解,同时给出了H∞鲁棒控制策略的显式表达式,最后给出数值算例验证了其可行性.
The problem of H∞ robust control design for Ito linear Markovian jump systems with noise dependent on state x (t), control u (t) and disturbance v (t) is studied by using the differential game theory. Firstly, the control variables u (t) is considered as one side of the game. The stochastic disturbance v (t) is regarded as the other side of the game, so that the H∞ robust control problem is transformed into a two-person zero-sum differential game problem. Then by analyzing this differential game problem The existence conditions of the H∞ robust control are obtained. The existence of solutions for the corresponding matrix Riccati algebraic equations is obtained. At the same time, an explicit expression of the robust control strategy for H∞ is given. Finally, a numerical example is given to verify its feasibility.