Showing papers by "Hassan K. Khalil published in 1981"
01 Dec 1981
TL;DR: In this paper, a quadratic-type Lyapunov function for a singularly perturbed system is obtained as a weighted sum of quadratically-type LSTM functions of two lower order systems.
Abstract: Asymptotic and exponential stability of nonlinear singularly perturbed systems are investigated via Lyapunov stability techniques. A quadratic-type Lyapunov function for a singularly perturbed system is obtained as a weighted sum of quadratic-type Lyapunov functions of two lower order systems. Estimates of domain of attraction, of upper bound on perturbation parameter, and of degree of exponential stability are obtained. The method is illustrated by studying the stability of a synchronous generator connected to an infinite bus.
257 citations
TL;DR: Singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time-invariant systems and it is shown that such a strategy may, in general, be destabilizing even when the neglected modes are asymptotically stable.
Abstract: Singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time-invariant systems. The effect of designing the control strategy using a model that neglects unknown parasitic elements is considered. It is shown that such a strategy may, in general, be destabilizing even when the neglected modes are asymptotically stable. Special structures that will not permit this situation and will guarantee asymptotic stability are illustrated.
94 citations
TL;DR: Estimates of the region of attraction and bounds on the small parameters are obtained and sufficient conditions are derived to guarantee the asymptotic stability of a class of nonlinear singularly perturbed systems with several perturbation parameters of the same order.
51 citations
TL;DR: In this article, sufficient conditions are derived to guarantee the asymptotic stability of a class of non-linear singularly perturbed systems with several perturbation parameters of the same order.
3 citations