INVARIANCES OF STRONGLY CONTINUOUS QUASI SEMIGROUPS AND DISTURBANCE DECOUPLING PROBLEMS

INVARIANCES OF STRONGLY CONTINUOUS QUASI SEMIGROUPS AND DISTURBANCE DECOUPLING PROBLEMS

S. Sutrima, M. Mardiyana, T. S. Martini

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Abstract

In this paper, invariances of a subspace of a Hilbert space under strongly continuous quasi semigroup (C0-quasi semigroup) are characterized. The invariance- relationship between the C0-quasi semigroups and its in nitesimal generator are also investigated including for the generator of Riesz-spectral operators. The invariant con- cepts for a non-autonomous system can also be characterized in the C0-quasi semigroup term. Some relationships of the invariances are also identi ed. The system-invariance is applicable to solve a disturbance decoupling problem of the non-autonomous linear control systems. The su ciency for the solvability is identi ed by the largest controlled invariant subspace of kernel of output operator. An example is simulated to con rm the disturbance decoupling problem of the non-autonomous linear control systems.

Keywords

invariant subspace, C0-quasi semigroup, system-invariance, disturbance de- coupling problem, solvable.