This paper applies three different control techniques to the design of a quarter car semiactive suspension system. The three techniques, originally developed to solve a constrained optimal control problem, are optimal gain switching, discontinuous variable structure control and explicit model predictive control. All of them divide the state space into convex regions and assign a linear or affine state feedback controller to each region. The partition of the state space is computed off-line. During the on-line phase, the controller switches between the subcontrollers according to the current state. All the above techniques gave satisfactory results when applied to the design of semiactive suspension systems. A detailed comparison in terms of computational complexity, performance and simplicity of the design is proposed in the paper. Published as: T. Paschedag, A. Giua, C. Seatzu, Constrained optimal control: an application to semiactive suspension systems, Int. Journal of Systems Sci...