Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches to solve these in case of small-scale dense coefficients, there is no approach available to compute solutions in the large-scale sparse setting. In this paper, we develop an iterative method to compute low-rank approximations of stabilizing solutions of large-scale sparse continuous-time algebraic Riccati equations with indefinite quadratic terms. We test the developed approach for dense examples in comparison to other established matrix equation solvers, and investigate the applicability and performance in large-scale sparse examples.

翻译：在与稳健控制器设计有关的应用中,具有无限期二次曲线术语的代数Riccati方程式起着重要作用。 虽然在小规模密集系数的情况下有许多既定的办法来解决这些问题,但是在大规模稀少的环境中,没有现成的办法来计算解决方案。 在本文中,我们开发了一种迭代方法,用来计算大规模稀薄连续代数立方方程式的低级稳定解决方案近似值,并具有无限期的二次曲线术语。我们测试了与其他既定矩阵方程式解算器相比的成熟方法,并调查大规模稀有实例的可适用性和性。