Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
Series of Abstractions for Hybrid Automata
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Counterexample-Guided Abstraction Refinement
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Convex Optimization
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Verification and Control of Hybrid Systems: A Symbolic Approach
Verification and Control of Hybrid Systems: A Symbolic Approach
Reachability for linear hybrid automata using iterative relaxation abstraction
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Verification of hybrid systems based on counterexample-guided abstraction refinement
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Progress on reachability analysis of hybrid systems using predicate abstraction
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Automatic abstraction refinement for timed automata
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
Abstraction Refinement for Stability
ICCPS '11 Proceedings of the 2011 IEEE/ACM Second International Conference on Cyber-Physical Systems
SpaceEx: scalable verification of hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Relational abstractions for continuous and hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Constraints for continuous reachability in the verification of hybrid systems
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Lyapunov abstractions for inevitability of hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Timed relational abstractions for sampled data control systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
HybridSAL relational abstracter
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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An embedded software controller is safe if the composition of the controller and the plant does not reach any unsafe state starting from legal initial states (in an unbounded time horizon). Linear systems -- specified using linear ordinary differential or difference equations -- form an important class of models for such control systems. We present a new decidability result for safety verification of linear systems. Our decidability result assumes that the set of initial states and the set of unsafe states satisfy some conditions. When the set of initial and unsafe states do not satisfy these conditions, they can be overapproximated by sets that do satisfy the conditions. We thus get a counterexample guided abstraction refinement (CEGAR) procedure for the unconstrained safety verification of linear systems. Our new procedure performs abstraction-refinement on the initial and unsafe region, and not on the system itself. We present the new procedure and describe experimental results that demonstrate its effectiveness.