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A verification methodology is described and evaluated to formally determine uncertain linear systems stability in digital controllers with considerations to the implementation aspects. In particular, this methodology is combined with the digital-system verifier (DSVerifier), which is a verification tool that employs Bounded Model Checking based on Satisfiability Modulo Theories to check the stability of digital control systems with uncertainty. DSVerifier determines the control system stability, considering all the plant interval variation set, together with the Finite Word-length (FWL) effects in the digital controller implementation; DSVerifier checks the robust non-fragile stability of a given closed-loop system. The proposed methodology and respective tool are evaluated considering non-fragile control examples from literature. Experimental results show that the approach used in this study is able to foresee fragility problems in robust controllers, which could be overlooked by other existing approaches due to underestimating of FWL effects.

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DepthK is a software verification tool that employs a proof by induction algorithm that combines k-induction with invariant inference. In order to efficiently and effectively verify and falsify safety properties in C programs, DepthK infers program invariants using polyhedral constraints. Experimental results show that our approach can handle a wide variety of safety properties in several intricate verification tasks.