The existense of almost I-universal regulators for linear plants in the absolute invariance problem was proved. Regular triangulations of non-convex polyhedra were researched (jointly with Y. R. Romanovsky). The solvability of the regular triangulations existense problem (with given Steiner points) in time, polynomially depending on the number of vertices was proved. It was proved that the existense of a regular triangulations depends only on Steiner points lying on the polyhedron's boundary. Control theory, nolinear dyanimcs, multi-agent and networked systems, functional analysis, computational geometry.
Main publications:
A.V. Proskurnikov, A. Matveev, M. Cao, “Opinion Dynamics in Social Networks With Hostile
Camps: Consensus vs. Polarization”, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 61:6 (2016), 1524–1536
A. Proskurnikov, A. Matveev, “Popov-Type Criterion for Consensus in
Nonlinearly Coupled Networks”, IEEE TRANSACTIONS ON CYBERNETICS, 45:8 (2015), 1537–1548
A. Proskurnikov, “Average consensus in networks with nonlinearly delayed couplings and switching topology”, Automatica, 49:9 (2013), 2928–2932
A. Proskurnikov, “Consensus in switching networks with sectorial nonlinear couplings: Absolute stability approach”, Automatica, 49:2 (2013), 488–495
V.A. Yakubovich, A.L. Fradkov, D.J. Hill,
A.V. Proskurnikov, “Dissipativity of T-Periodic Linear Systems”, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 52:6 (2007), 1039–1047
A. V. Proskurnikov, A. S. Matveev, “Tsypkin and Jury–Lee criteria for synchronization and stability of discrete-time multiagent systems”, Avtomat. i Telemekh., 2018, no. 6, 119–139; Autom. Remote Control, 79:6 (2018), 1057–1073
A. V. Proskurnikov, A. L. Fradkov, “Problems and methods of network control”, Avtomat. i Telemekh., 2016, no. 10, 3–39; Autom. Remote Control, 77:10 (2016), 1711–1740
A. V. Proskurnikov, S. E. Parsegov, “Problem of uniform deployment on a line segment for second-order agents”, Avtomat. i Telemekh., 2016, no. 7, 152–165; Autom. Remote Control, 77:7 (2016), 1248–1258
A. V. Proskurnikov, “Consensus in nonlinear stationary networks with identical agents”, Avtomat. i Telemekh., 2015, no. 9, 44–63; Autom. Remote Control, 76:9 (2015), 1551–1565
A. V. Proskurnikov, “Frequency-domain criteria for consensus in multiagent systems with nonlinear sector-shaped couplings”, Avtomat. i Telemekh., 2014, no. 11, 110–126; Autom. Remote Control, 75:11 (2014), 1982–1995
M. Yu. Zvagel'skii, A. V. Proskurnikov, Yu. R. Romanovskii, “Regular triangulations and Steiner points”, Algebra i Analiz, 16:4 (2004), 88–113; St. Petersburg Math. J., 16:4 (2005), 673–690
2002
7.
A. V. Proskurnikov, Yu. R. Romanovskii, “Regular triangulations of non-convex polytopes”, Uspekhi Mat. Nauk, 57:4(346) (2002), 185–186; Russian Math. Surveys, 57:4 (2002), 817–818
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