Equations Formulation for Switched LTI Systems

The use of such modulated sinks that are activated and deactivated at discrete time instances means that the underlying mathematical model is of the form of a DAE 

Let the moduli nij (f) e 0, 1 V f 0, y = 1. Hs, of the Us switching MTFs be grouped into a vector m t), the outputs Zi of all storage elements in integral causality, the inputs Zd of all storage elements in derivative causality and the outputs of resistors and switches be grouped into a descriptor vector x. The outputs of all modulated sinks activated at switching events are combined into a vector X. Let denote the vector of all system inputs. 

If it is assumed that the system under consideration can be described by a linear time-invariant model for the time spans between two discrete switching events then, starting from the partitioning of a bond graph model into fields as displayed in Fig. 2.16, a DAE system in the form 

for some time intervals, no residual sinks are switched on via an MTF, then the mathematical model takes the form 

2 Bond Graph Representations of Hybrid System Models 

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