Stability analysis for linear time-varying systems based on generalized orthogonal polynomials

In this paper, generalized orthogonal polynomials are directly used to investigate state transition matrix for linear time-varying systems. The approximated series of state transition matrix for such systems is constructed via generalized orthogonal polynomial expansion, and it is shown that the approximated series can retain many properties of state transition matrix under some conditions. Moreover, new criteria of stability for linear time-varying systems are given in terms of the approximated series, the criteria are easier to be tested than the known ones due to the computation advantages via generalized orthogonal polynomials expansion.