Constrained stabilization with an assigned initial condition set
Constrained stabilization with an assigned initial condition set
复制标题
具有指定初始条件集的约束稳定
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
S. Miani
中科院分区：
文献类型：
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作者：
F. Blanchini;F. Mesquine;S. Miani
研究了具有控制约束的线性离散系统的镇定问题。在给定的紧多面体集合中，给出了状态反馈控制器存在的充要条件，该控制器能使系统的状态从每个初始状态渐近地到达原点。这些条件可以通过线性规划来检验。结果表明，当问题有一个解决方案时，可以形成一个多面体函数，它原来是一个李雅普诺夫函数，如果一个适当的非线性反馈控制器。两个程序的构造的李雅普诺夫函数。第一个是基于稳定反馈补偿器存在的属性，当且仅当对于在集合的顶点上选择的每个初始条件，存在将状态驱动到其内部的开环控制。第二个过程是基于给定的多面体集的可控性区域的建设，这个过程也可以应用到系统的参数u…
The problem of stabilizing a linear discrete-time system with control constraints is considered. Necessary and sufficient conditions are given for the existence of a state feedback controller which drives the state to the origin asymptotically from every initial state in an assigned compact polyhedral set. These conditions can be checked via linear programming. It is shown that when the problem has a solution, a polyhedral function can be formed which turns out to be a Lyapunov function if a proper nonlinear feedback controller is applied. Two procedures are presented for the construction of the Lyapunov function. The first is based on the property that the stabilizing feedback compensator exists if and only if for every initial condition chosen on a vertex of the set there exists an open-loop control driving the state to its interior. The second procedure is based on the construction of the controllability regions to the given polyhedral set; this procedure can also be applied to systems with parameter u...