Abstract
The stabilization problem is considered in this study for a nonlinear system. It is shown that the stability analysis of nonlinear systems can be reduced into linear matrix inequality (LMI) problems. First, the neural-network (NN) model is employed to approximate a nonlinear system via the backpropagation algorithm. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. In terms of Lyapunov's direct method, a sufficient condition is provided to guarantee the stability of nonlinear systems. Based on this criterion, a model-based fuzzy controller is then designed to stabilize the nonlinear system and the H∞ control performance is achieved at the same time. Finally, two examples with numerical simulations are given to illustrate the control methodology.
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