Reach control problem: Well-posedness and structural stability

We study well-posedness and structural stability of the reach control problem (RCP) for affine systems. We demonstrate that the affine and piecewise affine feedbacks introduced in previous papers for solving RCP on a simplex are well-posed and structurally stable in the presence of small perturbations of system parameters. We also present general results on well-posedness and structural stability of RCP on polytopes by continuous state feedback. Some results echo classical findings on well-posedness for the robust regulator problem.