Bumpless H∞ control for periodic piecewise linear systems

This paper investigates the bumpless H∞ control problem based on exponential stability and L2-gain analyses for a class of periodic piecewise linear systems. A novel characterization of bumpless transfer among a variety of subsystem controllers satisfying some interpolation constraints is introduced. By utilizing adjustable interpolation functions and multiple Lyapunov functions, more flexibility is provided so as to guarantee a desirable closed-loop performance and trajectory smoothness. Since the problem formulated boils down to a feasibility problem involving nonlinear matrix inequalities, an iterative algorithm which solves a series of convex optimization problems is developed. Numerical examples are presented to show the validity of the proposed methods.