A parametric Lyapunov equation approach to low gain feedback design for discrete-time systems
A parametric Lyapunov equation approach to low gain feedback design for discrete-time systems
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DOI：
10.1016/j.automatica.2008.06.019
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Bin Zhou;Zongli Lin;G. Duan
中科院分区：
文献类型：
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作者：
Bin Zhou;Zongli Lin;G. Duan
低增益反馈是一种参数化的稳定状态反馈增益族，其增益随参数的减小而趋于零，在约束控制系统、鲁棒控制和非线性控制中有着广泛的应用。在连续时间环境下，目前有三种方法可以构造低增益反馈律：特征结构配置方法、基于参数ARE的方法和基于参数Lyapunov方程的方法。特征结构配置方法导致反馈增益在低增益参数中明确参数化。基于参数ARE的方法导致李雅普诺夫函数沿着反馈增益，但需要针对参数的每个值求解ARE。基于参数化李雅普诺夫方程的方法具有前两种方法的优点，并导致显式参数化的反馈增益和李雅普诺夫函数。前两种方法已扩展到离散时间设置。提出了一种基于参数李雅普诺夫方程的离散时间系统低增益反馈设计方法。
Low gain feedback, a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero, has found several applications in constrained control systems, robust control and nonlinear control. In the continuous-time setting, there are currently three ways of constructing low gain feedback laws: the eigenstructure assignment approach, the parametric ARE based approach and the parametric Lyapunov equation based approach. The eigenstructure assignment approach leads to feedback gains explicitly parameterized in the low gain parameter. The parametric ARE based approach results in a Lyapunov function along with the feedback gain, but requires the solution of an ARE for each value of the parameter. The parametric Lyapunov equation based approach possesses the advantages of the first two approaches and results in both an explicitly parameterized feedback gains and a Lyapunov function. The first two approaches have been extended to discrete-time setting. This paper develops the parametric Lyapunov equation based approach to low gain feedback design for discrete-time systems.