Gain Scheduling for Nonlinear Systems via Integral Quadratic Constraints

The paper considers a general approach for gain scheduling of Lipschitz continuous nonlinear systems. The approach is based on a linear parameter varying system (LPV) representation of the nonlinear dynamics along with integral quadratic constraints (IQC) to account for the linearization errors. Past results have shown that Jacobian linearization leads to hidden coupling terms in the controlled system. These terms arise due to neglecting the higher order terms of the Taylor series and due to the use of constant (frozen) values of the scheduling parameter. This paper proposes an LPV control synthesis method that accounts for these shortcomings. The higher order terms of the linearization are treated as a memoryless uncertainty whose input/output behavior is described by a parameter varying IQC. It is also shown that if the rate of the scheduling parameter is measurable then it can be treated as a known disturbance in the control synthesis step. A simple numerical example shows that the proposed control design approach leads to improved control performance.