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.
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