论文标题
在共轭离散时间代数riccati方程的最大解决方案上
On the maximal solution of the conjugate discrete-time algebraic Riccati equation
论文作者
论文摘要
在本文中，我们考虑了一类共轭离散时间Riccati方程，最初是由离散时间抗线性系统的线性二次调节问题引起的。在某些温和的假设和固定点迭代的框架下，为存在与共轭离散时间riccati方程的最大解决方案提供了建设性的证明，其中控制权重矩阵是非词性的，其常数术语是hermitian。此外，从合适的初始矩阵开始，我们还表明，由固定点迭代生成的非插入序列至少线性地收敛到Riccati方程的最大解。举例说明了我们的主要定理的正确性，并为对另一种有意义的解决方案的研究提供了相当大的见解。
In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under some mild assumptions and the framework of the fixed-point iteration, a constructive proof is given for the existence of the maximal solution to the conjugate discrete-time Riccati equation, in which the control weighting matrix is nonsingular and its constant term is Hermitian. Moreover, starting with a suitable initial matrix, we also show that the nonincreasing sequence generated by the fixed-point iteration converges at least linearly to the maximal solution of the Riccati equation. An example is given to demonstrate the correctness of our main theorem and provide considerable insights into the study of another meaningful solutions.
