Convergence and Stability Analysis of Nonlinear Singular Systems: Application to Circuit Network

A new class of singular linear time-invariant systems and electrical circuits are introduced. The manuscripts discusses the analytical study of the practical stability of linear time-invariant singular perturbed systems using Lyapunov techniques under the assumption that the initial conditions are consistent. The paper works out and proves the sufficient conditions (posed as LMIs) for practical stability of perturbed singular systems. Moreover, we study the problem of stability and stabilization of some classes of singular systems. Some illustrative numerical examples, in particular for circuit network, are given to illustrate the effectiveness of the proposed results.