Estabilidade em tempo finito de sistemas lineares com parâmetros variantes no tempo: abordagem aleatória

Abstract

The aim of this work is to develop a new strategy to check the finite-time stability of linear parameter-varying (LPV) systems. By applying the classical Lyapunov method, sufficient conditions are derived to ensure finite-time stability for larger classes of time-varying systems, extending beyond the scope of existing results. The concept of contractive stability in T-steps adapted to LPV systems has been developed. As the optimized contraction problem demands a prohibitive computational burden even for small values of T, a randomized approach is applied to solve it. The robust finite-time contractive stability of LPV systems in T-steps is tested in terms of a feasibility problem involving linear matrix inequalities (LMIs). The randomized approach is able to ensure the feasibility of the optimization problem with a high degree of probability, providing a test algorithm that guarantees the contractive stability of the system in T-steps within a finite time. The use of the Mayne’s algorithm, a specific case of Kalman filter, for the identification of MR damper has proved very beneficial, resulting in the system identification with an error of less than 0.001%. A controller was designed and adapted to an MR damper system coupled to a shaking table to experimentally validate the stability theories discussed in this work, resulting in data obtained from real-time experiments.