Generalized Gram Matrix and Its Application to the Observability Problem for Linear Nonsteady Systems

Sufficient conditions for the nondegeneracy of a generalized Gram matrix are obtained. In particular, it is shown that the generalized Gram matrix is nondegenerate for the Chebyshev systems of functions. An application of the results to the observability problems for linear nonsteady systems of ordinary differential equations are given. In terms of the observability matrix, necessary and sufficient conditions of the complete and total observability by means of finite-parameter solving operations are established.