Equivalent and sufficient stability conditions of linear discrete time-varying systems

The stability problem, including stability, asymptotical stability, uniformly asymptotical stability, and the stabilization of a linear discrete time-varying control system are discussed. Based on the system's fundamental matrix, the equivalent conditions ensuring the time-varying system to be some stability properties are obtained, and using inequality techniques, Some new sufficient stability and stabilization criteria are obtained, which are easily veryfied in system design. Some simulated examples show the effectiveness of the results obtained in the paper.