BMI-Based Stabilization of Linear Uncertain Plants With Polynomially Time Varying Parameters

This technical note considers the robust stabilization of uncertain linear time-varying continuous-time systems with a mode-switch dynamics. Each mode is characterized by a theoretically unbounded dynamical matrix containing elements whose time behavior over bounded time intervals is sufficiently smooth to be well described by interval polynomials of arbitrary degree. Using a parameter dependent Lyapunov function polynomially depending on time, the stabilizing controller for each single mode is directly obtained by the solution of some BMI´s, which become LMI´s by fixing two positive scalars. The stability conditions of the switching closed loop system are derived defining a switched Lyapunov function and involving the permanence time interval of the switching plant over each single mode. A salient feature of the technical note is that, unlike all the other existing methods, each plant mode can be stabilized over arbitrarily large uncertain domains of parameters and their derivatives.