Solution concepts for linear piecewise affine differential-algebraic equations
Résumé
In this paper, we introduce a definition of solutions for linear piecewise affine differential-algebraic equations (PWA-DAEs). Firstly, to address the conflict between projectorbased jump rule and active regions, we propose a concept called state-dependent jump path. Unlike the conventional perspective that treats jumps as discrete-time dynamics, we interpret them as continuous dynamics, parameterized by a virtual timevariable. Secondly, by adapting the hybrid time-domain solution theory for continuous-discrete hybrid systems, we define the concept of jump-flow solutions for PWA-DAEs with the help of Filippov solutions for differential inclusions. Subsequently, we study various boundary behaviors of jump-flow solutions. Finally, we apply the proposed solution concepts in simulating a state-dependent switching circuit.
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