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Linear Time Invariant (LTI) systems are ubiquitous in control applications.Unbounded-time reachability analysis that can cope with industrial-scale modelswith thousands of variables is needed. To tackle this problem, we use abstractacceleration, a method for unbounded-time polyhedral reachability analysis forlinear systems. Existing variants of the method are restricted to closedsystems, i.e., dynamical models without inputs or non-determinism. In thispaper, we present an extension of abstract acceleration to linear loops withinputs, which correspond to discrete-time LTI control systems under guardconditions. The new method relies on a relaxation of the solution of the lineardynamical equation that leads to a precise over-approximation of the set ofreachable states, which are evaluated using support functions. In order toincrease scalability, we use floating-point computations and ensure soundnessby interval arithmetic. Our experiments show that performance increases byseveral orders of magnitude over alternative approaches in the literature. Inturn, this tremendous gain allows us to improve on precision by computing moreexpensive abstractions. We outperform state-of-the-art tools for unbounded-timeanalysis of LTI system with inputs in speed as well as in precision.

Unbounded-Time Analysis of Guarded LTI Systems with Inputs by Abstract Acceleration (extended version)