摄动离散Riccati方程解的上下界估计

On the Estimation of Upper and Lower Bound for Solutions to Perturbed Discrete Riccati Equations

讨论摄动离散Riccati方程正定解的估计问题。针对摄动参数满足范数有界不确定性情形,获得了正定解的上界和下界,且界的计算通过确定的离散Riccati方程的解给出,避免高阶代数方程的求解,同时得到基于Riccati方程的摄动离散系统稳定性分析的新方法,所给出的数值算例验证了方法的可行性。

On the Estimation of Upper and Lower Bound for Solutions to Perturbed Discrete Riccati EquationsAbstract: The estimation of the positive definite solution of perturbed discrete Riccati equations is discussed.Several upper bounds and lower bounds of the positive definite solution are obtained under the condition that the perturbation parameters are norm-bounded uncertain.The calculation of the bounds are given by definite Riccati equation,thus it is avoided to solve high order algebraic equations.The validity of the method is validate by numerical examples.