A gain-scheduling control approach to stabilization of LTI systems with generalized saturation input

In this paper, we will present a gain-scheduling control method for designing output feedback laws that stabilize a linear system subject to generalized saturation input, which is composed of N(N ges 1) bends piecewise linear concave/convex functions. By exploiting the connection between one bend piecewise linear function and standard saturation function and expressing saturation on convex hull of linear functions, the design of output feedback control law will be solved as an optimization problem with LMI constraints. This approach will then be extended to multiple bends piecewise linear functions, by treating the multiple bends piecewise linear function as the convex combination of several one bend piecewise linear functions. This work will broaden the scope of gain-scheduling control approach to larger class of practical engineering problems