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Abstract. This paper deals with adaptive regulation of a discrete-time linear time-invariant plant witharbitrary bounded disturbances whose control input is constrained to lie within certain limits. The adaptivecontrol algorithm exploits the one-step-ahead control strategy and the gradient projection type estimationprocedure using the modified dead zone. The convergence property of the estimation algorithm is shown tobe ensured. The sufficient conditions guaranteeing the global asymptotical stability and simultaneously thesuboptimality of the closed-loop systems are derived. Numerical examples and simulations are presented tosupport the theoretical results.

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Introduction. The adaptive stabilization of some classes of uncertain multivariable static plants with arbitrary unmeasurable bounded disturbances is addressed in this article. The cases where the number of the control inputs does not exceed the number of the outputs are studied. It is assumed that the plant parameters defining the elements of its gain matrix are unknown. Again, the rank of this matrix may be arbitrary. Meanwhile, bounds on external disturbances are supposed to be known. The problem stated and solved in this work is to design adaptive controllers to be able to ensure the boundedness of the all input and output system's signals in the presence of parameter uncertainties. The purpose of the paper is to show that it is possible to stabilize any uncertain multivariable static plant which gain matrix may be either square or nonsquare and may have an arbitrary rank remaining unknown for the designer. Methods. The methods based on recursive point estimation of unknown plant parameters are utilized to design the adaptive inverse model-based controller. Results. The asymptotic properties of the adaptive controllers have been established. Simulation results have been presented to support the theoretic studies.

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