Discontinuous and adaptive control of nonnecessarily minimum phase linear systems

Relying on a combined approach based on both the theory of variable structure control systems (VSSs) and the theory of model reference adaptive control (MRAC), a novel scheme is presented which makes it possible to regulate uncertain LIT (linear time-invariant) SISO (single-input single-output) plants by solving a pole assignment control problem. This scheme has the advantage of being applicable even in the presence of nonminimum phase plants. By applying discontinuous control actions it is possible to force a signal which plays the role of output error to zero, keeping the amplitude of all the control signals bounded, and solving the prefixed regulation problem. The dynamics of the output error turns out to be of reduced order, and the explicit model, which needs to be used, is of first order. The case of bounded disturbances acting at the input of the plant is also dealt with and solved by the introduction of a further discontinuous control signal acting directly on the plant