Multiple-Mode Observer Design for a Class of Switched Linear Systems

Abstract

In this paper, the problems of state estimation are investigated for switched linear systems with average dwell time (ADT) switching in both continuous-time and discrete-time contexts. First, a set of mode-dependent Luenberger-type observers is designed subject to the ADT switching that is synchronous with the switching of the estimated systems. Then, a more practical case of the delayed observers is also considered, which implies that the switching of the multiple-mode observer to be designed has a lag to the switching of the estimated systems. In this case, the asynchronous switching signals are combined as a preliminary attempt, upon which sufficient conditions for the existence of the Luenberger-type observers and the corresponding ADT switching are formulated in terms of a set of linear matrix inequalities. Finally, the proposed approaches are applied to the state estimation of electronic circuits to demonstrate the effectiveness and applicability.Note to Practitioners-Switched systems are widely used for modeling complex systems, such as power electronics and network control systems, since they can complicatedly describe the interactions of a family of continuous-time or discrete-time dynamical systems. In practical systems, obtaining an accurate knowledge of the state is a crucial task that can determine the feasibility and reliability of subsequent activities as control. Usually, building a dynamical system called an "observer" to estimate the actual state is more applicable since some state variables cannot be measured through sensors. It is reasonable to design a multiple-mode observer for switched systems by designing a collection of observers for each mode of the switched system. If the active mode of the switched system is known, it is only to activate the corresponding mode of the observer. However, there is no guarantee that the estimation error will converge using this approach, even if the estimation error converges for each mode. Therefore, in this paper, the ADT switching is designed to guarantee that the estimation Manuscript error converges. Furthermore, in practice, it actually takes time to identify the system modes and apply the matched observer, which implies that the switching of the observers is asynchronous with that of the plants. In this case, the previously designed observer will fail to estimate the actual state. Thus, efficient design methods for the ADT switching and the delayed observers will also be developed to complete the estimation task.Index Terms-Multiple-mode observers, state estimation, switched linear systems. in

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“…On the other hand, time delays are the inherent features of many physical process and often a source of instability and poor performances. Since 1990s, switched systems with or without time delays have been extensively studied, and many useful results on observability and Luenberger-type observer design have been reported; see [11][12][13][14][15][16][17][18][19] and the references therein. However, few efforts are devoted to design observers for switched systems with UIs.…”