Periodic Lyapunov Equation Based Approaches to the Stabilization of Continuous-Time Periodic Linear Systems
Periodic Lyapunov Equation Based Approaches to the Stabilization of Continuous-Time Periodic Linear Systems
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DOI：
10.1109/tac.2011.2181796
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发表时间：
2012-08
影响因子：
6.8
通讯作者：
Bin Zhou;G. Duan
中科院分区：
文献类型：
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作者：
Bin Zhou;G. Duan
本文研究具有状态反馈的连续时间周期线性系统的镇定问题。该设计基于一类参数周期Lyapunov微分方程（PLDEs）的解，该微分方程是由保证收敛速率的最小能量控制问题引起的。通过仔细研究plde的特性及其解，设计了连续周期状态反馈。基于PLDE的方法对于CPL系统的稳定控制器设计是有效的，因为设计人员只需要求解一个线性微分方程，该方程的解在系统相对简单的情况下可以解析得到，在一般情况下可以通过积分进行数值计算。给出了PLDE中自由参数的充分必要条件，保证了闭环系统的稳定性，其特征乘法器集甚至可以精确计算。算例表明了该方法的有效性。
This note is concerned with stabilization of continuous-time periodic linear (CPL) systems with state feedback. The design is based on solutions to a class of parametric periodic Lyapunov differential equations (PLDEs) resulting from the problem of minimal energy control with guaranteed convergence rate. By carefully studying the properties of the PLDEs and their solutions, a continuous periodic state feedback is designed. The PLDE based approach is effective in designing stabilizing controller for CPL systems as the designers need only to solve a linear differential equation whose solution can be obtained analytically if the system is relative simple and can be computed numerically by integration in general cases. Necessary and sufficient conditions on the free parameter in the PLDE are proposed to guarantee the stability of the closed-loop system whose characteristic multiplier set can even be exactly computed accordingly. A numerical example is worked out to show the effectiveness of the proposed approach.