Difference and differential Riccati equations: a note on the convergence to the strong solution
Difference and differential Riccati equations: a note on the convergence to the strong solution
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DOI：
10.1109/9.148372
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发表时间：
1992-07
影响因子：
6.8
通讯作者：
G. Nicolao;M. Gevers
中科院分区：
文献类型：
--
作者：
G. Nicolao;M. Gevers
讨论了微分差分Riccati方程的解与相应的代数Riccati方程(ARE)的强解的收敛问题。在分析中只要求可检测性，而不对实虚轴上的特征值(在离散时间情况下，在单位圆上)进行假设。特别地，从结果可以得出，在唯一的可检测的假设下，一个正定的初始条件保证收敛到强解，即使在虚轴或单位圆上存在不可达的特征值。>；
The convergence of the solutions of the differential difference Riccati equations to the strong solution of the corresponding algebraic Riccati equation (ARE) is addressed. Detectability only is required in the analysis, and no assumption is made on the eigenvalues on the real imaginary axis (on the unit circle, in the discrete-time case). In particular, from the results, it follows that under the sole assumption of detectability, a positive definite initial condition guarantees convergence to the strong solution, even in the presence of unreachable eigenvalues on the imaginary axis or on the unit circle. >