Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Matrix computations (3rd ed.)
Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
Ellipsoidal Techniques for Reachability Analysis
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Inner and outer approximations of polytopes using boxes
Computational Geometry: Theory and Applications
Interval-valued reduced order statistical interconnect modeling
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Efficient representation and computation of reachable sets for hybrid systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Reachability of uncertain linear systems using zonotopes
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Approximate bisimulation relations for constrained linear systems
Automatica (Journal of IFAC)
Comparing forward and backward reachability as tools for safety analysis
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Reachability analysis of polynomial systems using linear programming relaxations
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
One-shot computation of reachable sets for differential games
Proceedings of the 16th international conference on Hybrid systems: computation and control
Reachability Analysis of Linear Systems with Stepwise Constant Inputs
Electronic Notes in Theoretical Computer Science (ENTCS)
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This paper presents a method for computing the reach set of affine systems for sets of initial states given as low-dimensional polytopes. An affine representation for polytopes is introduced to improve the efficiency of set representations. Using the affine representation, we present a procedure to compute conservative over-approximations of the reach set, which uses the Krylov subspace approximation method to handle large-scale affine systems (systems of order over 100).