Stabilization of Orthogonal Piecewise Linear Systems: Robustness Analysis and Design

In previous work the stabilization of Orthogonal Piecewise Linear (OPL) systems was considered and a simple design technique was outlined. In this paper the problems of robustness analysis and design for OPL systems are investigated. It is shown that, due to simplicity in the algebra involved, piecewise-linear Lyapunov functions offer considerable ease in addressing robustness. Assuming real structured parametric uncertainties in general affine linear state-space models, time-varying or state-dependent uncertainties as well as modeling errors can be taken into account, while retaining the same spirit in the design procedure. Bounds for the uncertain parameters can be easily found using linear programming and the computational complexity is kept low. These issues complete the OPL framework and confirm that it constitutes a simple design technique for addressing stability, performance and robustness while taking into account control limitations.