Stability Analysis for Linear Time-Varying Systems With Uncertain Parameters: Application to Steady-State Solutions of Nonlinear Systems

Abstract

The problem of robust stability in the state space model of linear time-varying systems with time- varying parameter uncertainties is considered. The Lyapunov approach is employed to obtain bounds on the uncertain time-varying parameters to guarantee the stability of the system. The robust stability bounds obtained are not necessarily symmetric with respect to the origin in the parameter space and can significantly reduce the conservatism in the previous results. Sufficient conditions for the stability of the steady-state responses of nonlinear systems (especially of piecewise linear systems) subjected to periodic excitations are proposed by using the results derived. Two numerical examples are used to demonstrate the accuracy of the formulation.

Uniformly asymptotic stability of second-order linear time-varying systems

“…24 Cao et al aimed at the second-order damped systems with nonlinear uncertainties, proposing asymptotic stability criterion based on the eigenvalue. 25 Diwekar et al considered the robust controller design according to the structured uncertainties. 26 With the arranged eigenvalue sequence, they proposed a simple procedure to select control gains which can guarantee the stability of the system.…”

Robust stability bounds for nonclassically damped systems with multi-directional perturbations

“…Most of previous results on robust stability are restricted to bounds on the parameter uncertainties in the state-space models, see, for example, Zhou and Khargonekar [1], Siljak [2], Bien and Kim [3], Gao and Antsaklis [4], Pun et al [5] and the literature cited therein. Even though any secondorder system can be represented as an equivalent first-order system, retaining the model in matrix second-order form has many advantages.…”