M. Gati and G. Ferrari-Trecate. Computation of observability regions for piecewise affine systems: A projection-based algorithm. Proc. 44th IEEE Conference on Decision and Control and European Control Conference 2005 , pages 6922--6927, 2005. Seville, Spain, 12-15 December.
In this paper we consider the problem of computing sets of observable states for discrete-time,piecewise affine systems. When the maximal set of observable states is full-dimensional, we provide an algorithm forreconstructing it up to a zero measure set. The core of the method is a quantifierelimination procedure that, in view of basic resultson piecewise linear algebra, can be performed via the projection ofpolytopes on subspaces.We also provide a necessary condition on the minimal length of the observability horizonin order to expect a full-dimensional set of observable states.Numerical experiments highlight that the new procedure is considerably faster than theone proposed in (Ferrari-Trecate and Gati, 2004).