## Issue 3 (189), article 2

DOI:https://doi.org/10.15407/kvt189.03.029

Kibern. vyčisl. teh., 2017, Issue 3 (189), pp.

Zhiteckii L.S., PhD (Engineering), Acting Head of the Department of Intelligent Automatic Systems

e-mail: leonid_zhiteckii@i.ua

Solovchuk K.Yu., Postgraduate Student

e-mail: solovchuk_ok@mail.ru

**International Research and Training Center for Information Technologies and Systems of the NAS of Ukraine and Ministry of Education and Science of Ukraine,**

Acad. Glushkova av., 40, Kiev, 03680, Ukraine

**DISCRETE-TIME STEADY-STATE CONTROL OF INTERCONNECTED SYSTEMS BASED ON PSEUDOINVERSION CONCEPT**

** Introduction.** The problem of controlling interconnected systems subjected to arbitrary unmeasurable disturbances remains actual up to now. It is important problem from both theoretical and practical points of view. During the last decades, the internal model control principle becomes popular among other methods dealing with an improvement of the control system. A perspective modification of the internal model control principle is the so-called model inverse approach. Unfortunately, the inverse model approach is quite unacceptable if the systems to be controlled are square but singular or if they are nonsquare. It turned out that the so-called pseudoinverse (generalized inverse) model approach can be exploited to cope with the noninevitability of singular square and also nonsquare system.

**of the paper is to generalize the results obtained by the authors in their last works which are related to the asymptotic properties of the pseudoinverse model-based method for designing an efficient steady-state control of interconnected systems with uncertainties and arbitrary bounded disturbances and also to present some new results.**

*The purpose***In this paper, the main effort is focused on analyzing the asymptotic properties of the closed-loop systems containing the pseudoinverse model-based controllers. In the framework of the pseudoinversion concept, new theoretical results related to the asymptotic behavior of these systems are obtained. Namely, in the case of nonsingular gain matrices with known elements, the upper bounds on the ultimate norms of output and control input vectors are found. Next, in the case of nonsquare gain matrices whose elements are also known, the asymptotic behavior of the feedback control systems designed on the basis of pseudoinverse approach are studied. Further, the sufficient conditions guaranteeing the boundedness of the output and control input signals for the linear and certain class of nonlinear interconnected systems in the presence of uncertainties are derived.**

*Results.**Conclusion.*It has been established that the pseudoinverse model-based concept can be used as a unified concept to deal with the steady-state regulation of the linear interconnected discrete-time systems and of some classes of nonlinear interconnected systems with possible uncertainties in the presence of arbitrary unmeasured but bounded disturbances.

*Keywords:**discrete time, feedback, pseudoinversion, interconnected systems, optimality, stability, uncertainty*.

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**Received** 17.02.2017