Theoretical Computer Science
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
Communication and Concurrency
On systematic simulation of open continuous systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Model checking LTL over controllable linear systems is decidable
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Dealing with Nondeterminism in Symbolic Control
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Bisimilar Finite Abstractions of Interconnected Systems
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Sampling-Based Resolution-Complete Algorithms for Safety Falsification of Linear Systems
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Approximately bisimilar symbolic models for nonlinear control systems
Automatica (Journal of IFAC)
Discrete-State Abstractions of Nonlinear Systems Using Multi-resolution Quantizer
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Approximately bisimilar symbolic models for digital control systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Input-output robustness for discrete systems
Proceedings of the tenth ACM international conference on Embedded software
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The use of bisimilar finite abstractions of continuous and hybrid systems, greatly simplifies complex computational tasks such as verification or control synthesis. Unfortunately, because of the strong requirements of bisimulation relations, such abstractions exist only for quite restrictive classes of systems. Recently, the notion of approximate bisimulation relations has been introduced, allowing the definition of less rigid relationships between systems. This relaxed notion should certainly allow us to build approximately bisimilar finite abstractions for more general classes of continuous and hybrid systems. In this paper, we show that for the class of stable discrete-time linear systems with constrained inputs, there exists an approximately bisimilar finite state system of any desired precision. We describe an effective procedure for the construction of this abstraction, based on compositional reasoning and samples of the set of initial states and inputs. Finally, we briefly show how our finite abstractions can be used for verification or control synthesis.