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This paper proposes an output-feedback sliding mode control design for a class of uncertain multivariable plants with nonlinear disturbances. The approach used here is based on the control parameterization employed in model-reference adaptive control. The disturbances are allowed to be unmatched and to depend not only on the plant output but also on its unmeasurable state. A less restrictive condition on the uncertainty of the high frequency gain matrix is also obtained.Lemma 4. Let r(t) be an absolutely continuous scalar function. Suppose r(t) is nonnegative and while r > 0 it satisfies r = ≤ −δγr + R exp(−λt) where δ, γ, λ,

Abstract-This paper considers the robust output tracking problem using a model-reference sliding mode controller for linear multivariable systems of relative degree one. It is shown that the closed loop system is globally exponentially stable and the performance is insensitive to bounded input disturbances and parameter uncertainties. The strategy is based on output-feedback unit vector control to generate sliding mode. The only required a priori information about the plant high frequency gain matrix Kp is the knowledge of a matrix Sp such that −KpSp is Hurwitz which relaxes the positive definiteness requirement usually needed by other methods.

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This study presents an output-feedback control algorithm based on unit vector sliding mode for a class of multivariable systems. The control objective is to force each output signal to track a desired reference trajectory, while retaining good performance despite parameter uncertainties, unmatched disturbances and actuators faults that eventually may occur in the plant. Owing to the new approach proposed to tackle this problem, which involves a linear matrix inequality to be satisfied by the control distribution matrix, no upper bound on this matrix is required. Moreover, a remarkable result is that the proposed fault-tolerant controller can even handle variations in the order of the system dynamics. The analysis shows that the resulting closed-loop system is globally exponentially stable. A simulation example with a chain of trailers driven by redundant actuators illustrates the design and effectiveness of the proposed strategy.

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Summary An adaptive sliding‐mode unit vector control approach based on monitoring functions to deal with disturbances of unknown bounds is proposed. An uncertain multivariable linear system is considered with a quite general class of nonsmooth disturbances. Global stabilization/tracking is demonstrated using either state or output feedback. The proposed adaptation method makes the control gain less conservative, becoming large enough when the disturbance grows and becoming smaller when it decreases, leading to reduced chattering effects. In contrast to previous methods, the new switching scheme is able to guarantee a prespecified transient time, maximum overshoot, and steady‐state error for multivariable uncertain plants. The proposed technique is applied to the trajectory tracking control of a surface vessel subjected to ocean currents, wind, and waves. Simulations are presented to show the performance of the new adaptation scheme in this adverse scenario of possibly growing, temporarily large, or vanishing exogenous disturbances.