On the Computation of Controlled Invariant and Output Invisible Subspaces for Parameter-dependent Systems

This paper proposes a new approach for computing controlled invariant and output invisible subspaces of parameter-dependent systems. Non-strictly proper systems are considered, and the system matrices can exhibit a polynomial dependence on the parameter. The proposed approach is applied in both contexts of constant and parameter-dependent inputs making the subspace invariant, referred to as the generalized or generalized adaptively controlled invariant and output invisible subspaces. A large discussion unifies and makes the link with several contributions to the literature. Moreover, a procedure to compute one of the parameter-dependent input trajectories is provided. A numerical example is presented to demonstrate the effectiveness of the strategy.