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On averaging for switched linear differential algebraic equations
"... Averaging is an effective technique which allows the analysis and control design of nonsmooth switched systems through the use of corresponding simpler smooth averaged systems. Approximation results and stability analysis have been presented in the literature for dynamic systems described by switch ..."
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Averaging is an effective technique which allows the analysis and control design of nonsmooth switched systems through the use of corresponding simpler smooth averaged systems. Approximation results and stability analysis have been presented in the literature for dynamic systems described by switched ordinary differential equations. In this paper the averaging technique is shown to be useful also for the analysis of switched systems whose modes are represented by means of differential algebraic equations (DAEs). An approximation result is derived for a simple but representative homogenous switched DAE with periodic switching signals and two modes. Simulations based on a simple electrical circuit model illustrate the theoretical result.
Linear switched DAEs: Lyapunov exponents, a converse Lyapunov Theorem, and Barabanov norms
"... Abstract — For linear switched differential algebraic equations (DAEs) we consider the problem of characterizing the maximal exponential growth rate of solutions. It is shown that a finite exponential growth rate exists if and only if the set of consistency projectors associated to the family of DA ..."
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Cited by 5 (5 self)
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Abstract — For linear switched differential algebraic equations (DAEs) we consider the problem of characterizing the maximal exponential growth rate of solutions. It is shown that a finite exponential growth rate exists if and only if the set of consistency projectors associated to the family of DAEs is product bounded. This result may be used to derive a converse Lyapunov theorem for switched DAEs. Under the assumption of irreducibility we show that a construction reminiscent of the construction of Barabanov norms is feasible as well. I.
An averaging result for switched DAEs with multiple modes
"... The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (OD ..."
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Cited by 3 (3 self)
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The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (ODEs) has been widely analyzed in the literature. The averaging approach can be useful also for the analysis of switched differential algebraic equations (DAEs). Indeed by analyzing the evolution of the switched DAEs state it is possible to conjecture the existence of an average model. However a trivial generalization of the ODE case is not possible due to the presence of state jumps. In this paper we discuss the averaging approach for switched DAEs and an approximation result is derived for homogenous switched linear DAE with periodic switching signals commuting among several modes. This approximation result extends a recent averaging result for switched DAEs with only two modes. Numerical simulations confirm the validity of the averaging approach for switched DAEs.
Stabilization of switched linear differential algebraic equations and periodic switching
 IEEE Trans. Autom. Control
"... AbstractWe investigate stabilizability of switched systems of differentialalgebraic equations (DAEs). For such systems we introduce a parameterized family of switched ordinary differential equations that approximate the dynamic behavior of the switched DAE. A criterion for stabilizability of a sw ..."
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AbstractWe investigate stabilizability of switched systems of differentialalgebraic equations (DAEs). For such systems we introduce a parameterized family of switched ordinary differential equations that approximate the dynamic behavior of the switched DAE. A criterion for stabilizability of a switched DAE system using timedependent switching is obtained in terms of these parameterized approximations. The tightness of the proposed criterion is analyzed.
Observer design for linear switched differentialalgebraic equations
, 2016
"... A dynamical system comprises a mathematical model of an underlying physical phenomenon. It has two basic components: external signals which interconnect the system with its environment and the internal state that evolves according to the model description. The external signals can usually further ..."
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A dynamical system comprises a mathematical model of an underlying physical phenomenon. It has two basic components: external signals which interconnect the system with its environment and the internal state that evolves according to the model description. The external signals can usually further be split into inputs and outputs. One of the basic problem associated with any dynamical system is that of constructing an observer which uses the available information of the external signals to estimate the internal state. The purpose of this project is to develop observers for dynamical systems modeled as switched differentialalgebraic equations (DAEs). The motivation to study this particular system class is twofold: 1) In contrast to ordinary differential equations (ODEs), DAEs include differential as well as algebraic equations. Practically every system’s model contains algebraic equations in the first place so it is natural to use DAEs (instead of the simplified ODEs) as a starting point. 2) Possible structural changes (like switches in electrical circuits or component faults in general physical system) can be modeled within the framework of switched systems. As an application of the proposed project, consider for example (national) electrical grids, which are large electrical circuits modeled as DAEs. An observer would then be used to monitor the energy flows through the transmission lines and could prevent overloading. Sudden structural changes in electrical grids are common and have to be taken into account; examples are: tripping of power lines due to harsh weather conditions, or a sudden drop in the energy production by wind turbines when whole wind parks are switched off in the presence of too strong winds. Hence a possible application of the theoretical results obtained by the proposed project could be improved monitoring tools for electrical grids.
Averaging for switched DAEs
"... Switched differentialalgebraic equations (switched DAEs) Eσ(t)ẋ(t) = Aσ(t)x(t) are suitable for modeling many practical systems, e.g. electrical circuits. When the switching is periodic and of high frequency, the question arises whether the solutions of switched DAEs can be approximated by an ave ..."
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Switched differentialalgebraic equations (switched DAEs) Eσ(t)ẋ(t) = Aσ(t)x(t) are suitable for modeling many practical systems, e.g. electrical circuits. When the switching is periodic and of high frequency, the question arises whether the solutions of switched DAEs can be approximated by an average nonswitching system. It is well known that for a quite general class of switched ordinary differential equations (ODEs) this is the case. For switched DAEs, due the presence of the socalled consistency projectors, it is possible that the limit of trajectories for faster and faster switching does not exist. Under certain assumptions on the consistency projectors a result concerning the averaging for switched DAEs is presented. Copyright line will be provided by the publisher 1