Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
The stability of saturated linear dynamical systems is undecidable
Journal of Computer and System Sciences
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
A Decidable Class of Planar Linear Hybrid Systems
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
A sound and complete proof rule for region stability of hybrid systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Abstraction Refinement for Stability
ICCPS '11 Proceedings of the 2011 IEEE/ACM Second International Conference on Cyber-Physical Systems
Model checking of hybrid systems: from reachability towards stability
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Lyapunov abstractions for inevitability of hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Complexity of stability and controllability of elementary hybrid systems
Automatica (Journal of IFAC)
Abstraction based model-checking of stability of hybrid systems
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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A rectangular switched hybrid system with polyhedral invariants and guards, is a hybrid automaton in which every continuous variable is constrained to have rectangular flows in each control mode, all invariants and guards are described by convex polyhedral sets, and the continuous variables are not reset during mode changes. We investigate the problem of checking if a given rectangular switched hybrid system is stable around the equilibrium point 0. We consider both Lyapunov stability and asymptotic stability. We show that checking (both Lyapunov and asymptotic) stability of planar rectangular switched hybrid systems is decidable, where by planar we mean hybrid systems with at most 2 continuous variables. We show that the stability problem is undecidable for systems in 5 dimensions, i.e., with 5 continuous variables.