2-Dimensional LTV System

We consider a 2-dimensional Linear Time-Varying (LTV) system with Time-Varying (TV) and Time-Invariant (TI) uncertainties. The dynamics is defined by the following ODE:

 \left\{\begin{array}{lcl} \dot{x} & = & -x - t y + t + u_1 + v_1 \\ \dot{y} & = & t^2 x + y - t + u_2 + v_2 \end{array}\right.

such that  v_1\in [-0.1,0.1], v_2\in [-0.1,0.1] are TV uncertainties and  u_1\in [-0.5,0.5], u_2\in [-0.5,0.5] are TI uncertainties.

We compute the symbolic flowpipes over the time horizon  [0,5] . The time cost is around 0.2 seconds. The following figure shows the octagon overapproximations for the concretized flowpipes w.r.t. the initial set  x(0) \in [1,1.5], y(0) \in [5,5.5] .

2dltv

By changing the initial set in the output file (.flow file), we are able to reuse the symbolic flowpipes and obtain the concretized flowpipes for another initial set  x(0) \in [-1.5,-1], y(0) \in [-5.5,-5] .

2dltv2

[Model file]

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