Compensation law for constrained systems with initial state uncertainty based on piecewise affine function

This paper considers a method for designing a compensation law for constrained linear systems with initial state uncertainty. By introducing a decomposition technique for finite-horizon linear systems, we derive a compensation law that satisfies system constraints under initial state uncertainty of a plant. The compensation law is characterized by a piecewise affine function of the available plant state. A numerical example is presented for illustrating the proposed compensation law.