**MSC2010** 39A30

### Stabilization of a multiconnected controlled continuous discrete system with non-overlapped decompositions with respect to part of variables

#### E. A. Kaledina^{1}

Annotation | This paper considers a multi-connected controllable system with non-overlapping decompositions. Given that most of the control laws are implemented on digital controllers, the control of the system is implemented as a piecewise-constant function. Multiconnectivity of the system, in turn, makes it impossible to use centralized control. Every isolated subsystem must work stably, and intersystem connections can have a destabilizing effect. In this case, piecewise-constant control is constructed as two-level, i.e. in the form of a sum of local and global control. Local control stabilizes the equilibrium positions of individual linear subsystems. Global control acts on intersystem connections. Conditions are obtained under which local control stabilizes linear subsystems, and the equilibrium position of the original multi-connected system is asymptotically stable in part of variables. |
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Keywords | multivariable dynamic system, piecewize-constant control, two-level control, asymptotic stability in part of variables, stabilization |

^{1}**Elena A. Kaledina**, Senior Teacher, Department of Applied Mathematics, Differential Equations and Theoretical Mechanics, National Research Mordovia State University (68 Bolshevistskaya Str., Saransk 430005, Republic of Mordovia, Russia), Ph.D. (Physics and Mathematics), ORCID: https://orcid.org/0000-0002-0992-9540, elena.lizina@gmail.com

**Citation**: E. A. Kaledina, "[Stabilization of a multiconnected controlled continuous discrete system with non-overlapped decompositions with respect to part of variables]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,22:3 (2020) 268–279 (In Russian)

**DOI** 10.15507/2079-6900.22.202003.268-279