The l1 Filter for Discrete-Time Switched Singular Positive Systems With Time-Varying Delays
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摘要: 该文主要研究了一类具有时变时滞的离散时间切换奇异系统在正性约束下的l1滤波器的设计问题.通过构造合适的共正Lyapunov函数并且利用平均驻留时间的方法, 以线性规划的形式给出使得相应的滤波误差系统是正的、正则的、因果的、指数稳定的充分条件.另外, 外部扰动输入对系统性能的影响也被加以分析和讨论, 并在稳定性的基础上进一步给出滤波误差系统具有给定l1增益性能的充分条件和相应滤波器的设计方法.最后, 通过数值算例来验证所给方法的有效性和可行性.Abstract: The design problem of l1 filters was studied for a class of discrete-time switched singular systems with positive constraints and time-varying delays. Through construction of an appropriate co-positive Lyapunov function and with the average dwell time technique, sufficient conditions in the form of linear programming were provided to ensure the corresponding filtering error system to be positive, regular, causal and exponentially stable. In addition, the effect of the exogenous disturbance input on the system performance was also analyzed and discussed. The sufficient conditions and design mechanisms for the corresponding filter to ensure that the filtering error system has the prescribed l1 disturbance attenuation performance were also given. Finally, a simulation example was provided to verify the effectiveness and feasibility of the proposed method.
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图 1 例1中的切换序列
注 为了解释图中的颜色，读者可以参考本文的电子网页版本.
Figure 1. The switching sequence in example 1
图 2 在w(k)≡0时, 系统(4)中状态x(k)的轨迹
注 为了解释图中的颜色，读者可以参考本文的电子网页版本.
Figure 2. Trajectory x(k) of system (4) with w(k)≡0
图 3 在w(k)≡0时, 系统(4)中状态xe(k)的轨迹
注 为了解释图中的颜色，读者可以参考本文的电子网页版本.
Figure 3. Trajectory xe(k) of system (4) with w(k)≡0
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