Compensation law for constrained systems based on a decomposition of finite-horizon linear systems

This paper considers a compensation law for constrained continuous-time linear systems. We introduce singular value decomposition (SVD) of finite-horizon linear systems and provide a compensation law which satisfies system constraints based on the SVD. The SVD allows us to construct basis functions consisting of dominant input-output signals where an auxiliary dynamical system is newly introduced so that it generates useful basis functions. The properties of the resulting system with compensation law are discussed, and the features of the proposed method are demonstrated by numerical examples.