A Piecewise Control Synthesis Approach for Nonlinear Systems with application to Hypersonic Vehicle

A Novel Approach has been presented for the control of nonlinear systems by the piecewise affine envelope method. By the computation of the piecewise affine envelope, the nonlinear control design problem has been reformulated as the control design problem of piecewise affine differential inclusions (PWADIs). Then, with the help of piecewise Lyapunov function theory, the H
_∞
control synthesis conditions for PWADIs can be formulated as the solving process of linear matrix inequalities. On the other hand, considering the hypersonic vehicles are complex nonlinear systems with uncertain dynamics, the proposed piecewise envelope control synthesis approach is applied to air-breathing hypersonic vehicles, the simulation results demonstrate the validity of the designed piecewise controller.