[AUD-011][High] Propagate LU failure in continuous-to-discrete conversion

[gabrielsantosphilips]

Audit finding

• ID: AUD-011
• Status: Verified defect
• Severity: High
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

ContinuousToDiscrete::Invert() discards the Boolean result of LuDecomposition::Decompose() and calls Inverse() unconditionally.

Source:

numerical-toolbox-cpp/numerical/control_analysis/ContinuousToDiscrete.hpp

Lines 47 to 53 in 2f47932

	math::SquareMatrix<T, StateSize>
	ContinuousToDiscrete<T, StateSize, InputSize, OutputSize>::Invert(const math::SquareMatrix<T, StateSize>& a)
	{
	solvers::LuDecomposition<T, StateSize> lu{};
	lu.Decompose(a);
	return lu.Inverse();
	}

Reproduction

For scalar A=2 and Ts=1, Tustin requires inversion of 2I/Ts - A = 0. UBSan reports division by zero in the upper-triangular solve, while Convert() returns normally.

Acceptance criteria

• Failed factorization is propagated as std::optional or explicit status.
• Tustin and backward-Euler validate finite positive sample time and singular operators.
• No inverse/factor accessor can be used after failed decomposition.
• Add singular and near-singular conversion tests with independent expected failure.