POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Rigorous Error Bounds for the Optimal Value in Semidefinite Programming
SIAM Journal on Numerical Analysis
The pitfalls of verifying floating-point computations
ACM Transactions on Programming Languages and Systems (TOPLAS)
The Zonotope Abstract Domain Taylor1+
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Combination of abstractions in the ASTRÉE static analyzer
ASIAN'06 Proceedings of the 11th Asian computing science conference on Advances in computer science: secure software and related issues
Computing relaxed abstract semantics w.r.t. quadratic zones precisely
SAS'10 Proceedings of the 17th international conference on Static analysis
Static analysis of finite precision computations
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Compositional analysis of floating-point linear numerical filters
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Modeling, optimization and computation for software verification
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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Embedded system control often relies on linear systems, which admit quadratic invariants. The parts of the code that host linear system implementations need dedicated analysis tools, since intervals or linear abstract domains will give imprecise results, if any at all, on these systems. Previous work by FERET proposes a specific abstraction for digital filters that addresses this issue on a specific class of controllers. This paper aims at generalizing the idea. It works directly on system representation, relying on existing methods from control theory to automatically generate quadratic invariants for linear time invariant systems, whose stability is provable. This class encompasses n-th order digital filters and, in general, controllers embedded in critical systems. While control theorists only focus on the existence of such invariants, this paper proposes a method to effectively compute tight ones. The method has been implemented and applied to some benchmark systems, giving good results. It also considers floating points issues and validates the soundness of the computed invariants.