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首页> 外文期刊>IEEE Transactions on Automatic Control >Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions
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Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions

机译：通过集诱导的Lyapunov函数对不确定离散时间系统进行最终有界控制

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摘要

In this note, linear discrete-time systems affected by both parameter and input uncertainties are considered. The problem of the synthesis of a feedback control, assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence, is investigated. It is shown that the problem has a solution if and only if there exists a certain Lyapunov function which does not belong to a preassigned class of functions (e.g., the quadratic ones), but it is determined by the target set in which ultimate boundedness is desired. One of the advantages of this approach is that we may handle systems with control constraints. No matching assumptions are made. For systems with linearly constrained uncertainties, it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets. The resulting compensator may be implemented as a linear variable-structure control.
机译：在本说明中，考虑了受参数和输入不确定性影响的线性离散时间系统。研究了反馈控制的综合问题，该问题可确保系统状态最终限制在给定的紧凑集合内，该紧凑集合包含具有指定收敛速度的起点。结果表明，只有当存在不属于预先指定的函数类（例如二次函数）的某个Lyapunov函数时，问题才可以解决，但是它由目标集确定，其中最终有界性是想要的。这种方法的优点之一是我们可以处理具有控制约束的系统。没有做出匹配的假设。对于具有线性约束不确定性的系统，表明可以通过涉及多面体集的数值有效算法来推导此类函数。所得补偿器可以被实现为线性可变结构控制。

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