Determinability and state estimation for switched differential-algebraic equations

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• 作者：Aneel Tanwani^a ; ^{aneel.tanwani@laas.fr}Author Vitae ; Stephan Trenn^b ; ^{trenn@mathematik.uni-kl.de}Author Vitae
• 关键词：Observer design ; Switched systems ; Differential&ndash ; algebraic equations ; Descriptor systems
• 刊名：Automatica
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：76
• 期：Complete
• 页码：17-31
• 全文大小：803 K
• 卷排序：76

文摘

The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential–algebraic equations (DAEs). Since this system class imposes time-varying dynamic and static (in the form of algebraic constraints) relations on the evolution of state trajectories, an appropriate notion of observability is presented which accommodates these phenomena. Based on this notion, we first derive a formula for the reconstruction of the state of the system where we explicitly obtain an injective mapping from the output to the state. In practice, such a mapping may be difficult to realize numerically and hence a class of estimators is proposed which ensures that the state estimate converges asymptotically to the real state of the system.