The quadratic stabilization problem for LTV plants with arbitrary mode-switch dynamics and non uniformly bounded parametric uncertainties

This paper considers the quadratic stabilization of linear time-varying (LTV) continuous-time plants with a switch-mode dynamics and non uniformly bounded parametric uncertainties. To this purpose, the trajectories of the time varying uncertain parameters are assumed to be described by polynomial functions of arbitrary degree. This extra information on the parameters dynamics allows the parametric uncertainty to be transferred in a polytopic region of the coefficient space. At some isolated time instants the parameters trajectories can exhibit some first kind discontinuities due e.g. to sharply varying operating conditions. The coefficients of the polynomials are unknown and time varying inside known bounded intervals. Using a parameter independent Lyapunov function, a quadratically stabilizing dynamic output controller is directly obtained by the solution of some LMIs.