On robust adaptive control of switched linear systems

Abstract

This paper investigates robust adaptive control of uncertain switched linear systems considering disturbances. Two modifications of the adaptive law of switched linear systems [1] based on parameter projection and a leakage approach are developed to guarantee the stability of the closed-loop switched
linear system: a projection law that requires knowledge of the bounds of the parameter estimates; and a leakage law based on initial conditions of the parameter estimates that does not require knowledge of the bounds of the parameter estimates. The closed-loop switched linear system is shown to be
globally uniformly ultimately bounded. In addition, the ultimate bounds of both adaptive control schemes are also given. A numerical example is provided to illustrate the effectiveness of the proposed methods.