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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.

This paper presents a novel, complete, and flexible optimization algorithm, which relies on recursive executions that re-constrains a model-checking procedure based on Satisfiability Modulo Theories (SMT). This SMT-based optimization technique is able to optimize a wide range of functions, including non-linear and non-convex problems using fixed-point arithmetic. Although SMT-based optimization is not a new technique, this work is the pioneer in solving non-linear and non-convex problems based on SMT; previous applications are only able to solve integer and rational linear problems. The proposed SMT-based optimization algorithm is compared to other traditional optimization techniques. Experimental results show the efficiency and effectiveness of the proposed algorithm, which finds the optimal solution in all evaluated benchmarks, while traditional techniques are usually trapped by local minima.

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