Factor C2D out into a library for reuse

Hybrid State Feedback Loop already has an implementation.  Grab it.

Change-Id: I8b294e3ee7d82249cbd2b0c732086a735a57c36b
diff --git a/frc971/control_loops/c2d.h b/frc971/control_loops/c2d.h
new file mode 100644
index 0000000..453a6a5
--- /dev/null
+++ b/frc971/control_loops/c2d.h
@@ -0,0 +1,39 @@
+#ifndef FRC971_CONTROL_LOOPS_C2D_H_
+#define FRC971_CONTROL_LOOPS_C2D_H_
+
+#include <chrono>
+
+#include <Eigen/Dense>
+
+namespace frc971 {
+namespace controls {
+
+template <typename Scalar, int num_states, int num_inputs>
+void C2D(const ::Eigen::Matrix<Scalar, num_states, num_states> &A_continuous,
+         const ::Eigen::Matrix<Scalar, num_states, num_inputs> &B_continuous,
+         ::std::chrono::nanoseconds dt,
+         ::Eigen::Matrix<Scalar, num_states, num_states> *A,
+         ::Eigen::Matrix<Scalar, num_states, num_inputs> *B) {
+  // Trick from
+  // https://en.wikipedia.org/wiki/Discretization#Discretization_of_linear_state_space_models
+  // to solve for A and B more efficiently.
+  Eigen::Matrix<Scalar, num_states + num_inputs, num_states + num_inputs>
+      M_state_continuous;
+  M_state_continuous.setZero();
+  M_state_continuous.template block<num_states, num_states>(0, 0) =
+      A_continuous *
+      ::std::chrono::duration_cast<::std::chrono::duration<Scalar>>(dt).count();
+  M_state_continuous.template block<num_states, num_inputs>(0, num_states) =
+      B_continuous *
+      ::std::chrono::duration_cast<::std::chrono::duration<Scalar>>(dt).count();
+
+  Eigen::Matrix<Scalar, num_states + num_inputs, num_states + num_inputs>
+      M_state = M_state_continuous.exp();
+  *A = M_state.template block<num_states, num_states>(0, 0);
+  *B = M_state.template block<num_states, num_inputs>(0, num_states);
+}
+
+}  // namespace controls
+}  // namespace frc971
+
+#endif  // FRC971_CONTROL_LOOPS_C2D_H_