Continuous-time Variables Research Articles

Decoupling of and inverses for time-varying linear systems

Attention is given to time-varying linear dynamic systems of a discrete or continuous time variable. For this class of systems the question of the existence and form of an inverse system is analyzed together with the question of decoupling a fixed plant by state variable feedback. It is shown that recent results (see [1], [2]) on the decoupling of stationary systems have a partial counterpart in the setting of nonstationary systems. A synopsis of the main results may be obtained by reading Theorem 1 and its corollaries.

A transform technique for time-varying linear hybrid systems

A computationally oriented transform technique for the analysis of time-varying linear systems involving both discrete-time (i.e., sampled-data) variables and continuous-time variables is presented in this paper. Finite-dimensional representations are described for the various linear operators involved, and methods for obtaining singular-value decompositions of these operators are given. The three parts of the singular-value decomposition are analogous to the direct transform, transfer function, and inverse transform of Laplace and Fourier transforms, and offer analogous insights into analysis and synthesis problems. An example is included to illustrate the analysis procedures.