Bumpless transfer control for switched systems: A time-and state-dependent multiple Lyapunov function method

For switched systems, the time-and state-dependent multiple Lyapunov function method is set up to investigate the bumpless transfer control problem. The key point of the proposed study is to relax the decreasing assumption of traditional Lyapunov functions at switching points and the global limitation of the bumpless transfer constraint, which provides more freedom for solving the bumpless transfer control problem. First, the description of the bumpless transfer performance is proposed by using switching points directly, which makes the controller only constrain in the subinterval of the active interval rather than the whole active interval. Second, a switching controller with time-varying gain matrices and a mixed dwell time-and state-dependent switching signal are designed to reduce control bumps and avoid frequent switching. Third, based on the developed multiple Lyapunov function method, a solvability condition of the bumpless transfer control problem is developed. Finally, an example is given to show the availability of the bumpless transfer control strategy.