Abstract
The £2 disturbance attenuation control or the nonlinear H∞ control of a nonlinear system requires solving the Hamilton-Jacobi-Isaacs (HJI) partial differential inequality, which is generally a difficult undertaking. Though there are inverse optimal approaches, they have limited utilization from a practical point of view. In this work, a novel approach of state feedback H∞ control is proposed for scalar nonlinear systems using piecewise affine bounds of scalar-valued nonlinear functions. An LMI based systematic procedure is proposed. To illustrate the proposed method, an example of a scalar nonlinear system possessing significant nonlinearity has been considered. To demonstrate the effectiveness of the proposed scheme, it is compared with Linear Parameter Varying (LPV) based state feedback H∞ control, using quasi-LPV models based on Taylor series expansion.
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