[AUD-003][Critical] Include D12 in H-infinity state-feedback synthesis

[gabrielsantosphilips]

Audit finding

• ID: AUD-003
• Status: Verified defect
• Severity: Critical
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

The public generalized plant accepts D12, but BuildAugmented() never reads it and hardcodes the control weight to identity. For z = C1 x + D12 u, synthesis requires the D12^T D12 control term and the C1^T D12 cross-term. Changing D12 therefore cannot change the controller, so the implementation solves a different game from the advertised model.

Source:

numerical-toolbox-cpp/numerical/robust_control/HInfinityStateFeedback.hpp

Lines 19 to 37 in 2f47932

	std::size_t DisturbanceSize,
	std::size_t ControlSize,
	std::size_t ErrorSize>
	struct GeneralizedPlant
	{
	static_assert(std::is_floating_point_v<T>, "GeneralizedPlant supports floating-point types");
	using StateMatrix = math::SquareMatrix<T, StateSize>;
	using DisturbanceMatrix = math::Matrix<T, StateSize, DisturbanceSize>;
	using ControlMatrix = math::Matrix<T, StateSize, ControlSize>;
	using ErrorStateMatrix = math::Matrix<T, ErrorSize, StateSize>;
	using ErrorControlMatrix = math::Matrix<T, ErrorSize, ControlSize>;
	StateMatrix A{};
	DisturbanceMatrix B1{};
	ControlMatrix B2{};
	ErrorStateMatrix C1{};
	ErrorControlMatrix D12{};
	};

and

numerical-toolbox-cpp/numerical/robust_control/HInfinityStateFeedback.hpp

Lines 96 to 112 in 2f47932

	typename HInfinityStateFeedback<T, StateSize, DisturbanceSize, ControlSize, ErrorSize>::Augmented
	HInfinityStateFeedback<T, StateSize, DisturbanceSize, ControlSize, ErrorSize>::BuildAugmented(T g) const
	{
	Augmented aug{};
	aug.B.SetBlock(plant.B2, 0, 0);
	aug.B.SetBlock(plant.B1, 0, ControlSize);
	auto controlWeight = math::SquareMatrix<T, ControlSize>::Identity();
	auto disturbanceWeight = math::SquareMatrix<T, DisturbanceSize>::Identity();
	disturbanceWeight *= -(g * g);
	aug.Rtilde.SetBlock(controlWeight, 0, 0);
	aug.Rtilde.SetBlock(disturbanceWeight, ControlSize, ControlSize);
	aug.Q = plant.C1.Transpose() * plant.C1;
	return aug;
	}

Feasibility additionally checks only diagonal signs and permits an absolute Riccati residual up to 1.

Acceptance criteria

• Implement the generalized D12 and cross-term formulation, or narrow the public API to the actually supported normalization.
• Use valid definiteness checks rather than diagonal-only tests.
• Use a scale-aware Riccati residual tolerance.
• Add an independent test where changing D12 changes the synthesized gain and achieved bound.