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In this paper we analyze the inverted pendulum system and use variable structure theory in controlling the car position and pendulum angle. We use Lyapunov theory getting the sliding mode function and output expression of the controller. At the same time we prove the astringency of sliding mode. The simulation and inverted pendulum system experiment both prove that the nonlinear variable structure...
Stabilization for a collection of feedback linearizable systems with uncertain parameter is dealt with in this paper. Necessary and sufficient conditions for a quadratic control Lyapunov function to be a common control Lyapunov function for these systems are obtained. A continuous state feedback control is designed based on the common control Lyapunov function. It can simultaneously stabilize these...
The stability and the domain of attraction of autonomous nonlinear systems are important properties to be determined. This paper aims at examining a computational method for estimating the domain of attraction of nonlinear system. This very method is based on the concept of a maximal Lyapunov function candidate. The studied algorithm yields a rational Lyapunov function candidate Vm where its the derivative...
In this paper, we show discretized Lyapunov functions for various nonlinear dynamical systems by using the method that the authors have proposed. We use Kushner's scheme of difference approximation with directions and Alcaraz et al.'s quantization of Markov processes to approximate Lyapunov equations by linear Schroumldinger-like equations. We construct time-invariant functions concerned with the...
This paper deals with the stability of solutions of nonlinear control systems in the entire phase space. It is shown that for determining the global stability of motion, it is necessary to first obtain a single scalar equation from the specified system, and only then apply the Hurwitz conditions. In the derived scalar equations corresponding to the initial system, both nonlinear functions and their...
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