Indefinite Robust Linear Quadratic Optimal Regulator for Discrete-Time Uncertain Singular Markov Jump Systems
针对离散时间不确定奇异马尔可夫跳变系统，通过罚函数法构造新代价函数，将无界鲁棒最优调节问题转化为正定加权矩阵的鲁棒最优调节问题，并给出最优状态反馈的存在条件与解析形式，保证闭环系统的正则性、因果性和随机稳定性。
The robust LQ optimal regulator problem for discrete-time uncertain singular Markov jump systems (SMJSs) is solved by introducing a new quadratic cost function established by the penalty function method, which combines the penalty function and the weighting matrices. First, the indefinite robust optimal regulator problem for uncertain SMJSs is transformed into the robust optimal regulator problem with positive definite weighting matrices for uncertain Markov jump systems (MJSs). The transformed robust LQ problem is settled by the robust least-squares method, and the condition of the existence and analytic form of the robust optimal regulator are proposed. On the infinite horizon, the optimal state feedback is obtained, which can guarantee the regularity, causality, and stochastic stability of the corresponding optimal closed-loop system and eliminate the uncertain parameters of the closed-loop system. A numerical example and a practical example of DC motor are used to verify the validity of the conclusions.