Invariances of strongly continuous quasi semigroups and disturbance decoupling problems

Abstract

In this paper, invariances of a subspace of a Hilbert space under strongly continuous quasi semigroup (C?-quasi semigroup) are characterized. The invariancerelationship between the C?-quasi semigroups and its infinitesimal generator are also investigated including for the generator of Riesz-spectral operators. The invariant concepts for a non-autonomous system can also be characterized in the C?-quasi semigroup term. Some relationships of the invariances are also identified. The system-invariance is applicable to solve a disturbance decoupling problem of the non-autonomous linear control systems. The sufficiency for the solvability is identified by the largest controlled invariant subspace of kernel of output operator. An example is simulated to confirm the disturbance decoupling problem of the non-autonomous linear control systems.