*Dynamical Systems:*descriptor systems, hybrid** **difference-differential systems, systems with** **after-effect, neutral time-delay systems, differential-algebraic systems with delay (DAD** **systems), 2-D systems ** **(*initial-valued problems, variation-of-constants formulae, series representations and exponential estimate of solutions, Laplace transform, algebraic properties of shift operator, generalized Caley-Hamilton theorems, dynamical systems models in practice*);

*Qualitative Control and Observations Theory:***control, reconstruction, canonical forms, controllability and observability, duality, realization and scale realizability, integer function of exponential type in control theory, Paley-Wiener theorem;**

*Industrial Mathematics Methods*;**: effective training mathematics didactic methods**

*Didactics***GRANTS**

** Belarus Education Ministry and National Academy of Science** Project Grants (

*project manager*

*and principal investigator*):

**GB 11-174:** *Qualitative characteristics** investigation in dynamic discrete-continuous systems of control** * (2011-2015),

**GB 26-101: ***The qualitative control theory investigations of hybrid difference-differential systems and its applications* (2006- 2010),

**GB 21-085: ***Analysis of properties and solutions of hybrid systems and its applications* (2002- 2005),

**GB 21-036: ***Development of the qualitative control and observation theory for systems with **impulse effects* (2001-2002),

**GB 96-044: ***Development some questions of the qualitative control theory for systems with d**eviating argument* *unsolved with respect to the derivative”* (1996-1998);

** Belarus Education Ministry** Project Grants (

*project manager*

*and principal investigator*):

“*Development of new methods for the investigation of qualitative characteristics of descriptor systems”* (1994-1995);

**GB 98-011: ***Level organization** of educational process on mathematical disciplines for technical specialties of universities* (2010),

**GB 98-011: ***Mathematical** study of the theory of control in hybrid systems* (1998-1999);

** Bialystok University of Technology** Grants (

*project manager*

*and principal investigator*):

**W/IMF/3/05****:** *Observability problems for nonlinear systems with delay* (2005-2006);

**W/IMF/3/03****:** *Problems** of observability of nonlinear systems with delay* (2003-2004);* * * *

**W/IMF/4/02:** *Time-Delay Systems of Control and Observation* (2002);

** Belarus Science and Technology Information** Fund Grant (

*project manager*

*and principal investigator*):

**BS 99-097:** *Development of dynamic systems of control by technological thermodynamics **processes with delay information and diffusion parameters* (1999-2000);

** International Federation on Automatic Control** 13

^{th}Congress Grant (1996);

** International Science Foundation** Project Grant 300+MW 3300 (1994-1995,

*as a member*

*of team)*;

** Individual International Science** (Soros) Foundation Grant (1993);

** Belarus Fund of Fundamental Investigation** Project Grant (

*project manager*

*and principal investigator*):

**F-39-387:** *Development of the qualitative control and observation theory for systems with **after-effect on the base of the minimal state space method * (1992-1994)

**SCIENTIFIC PARTNERS**

** Leading Belarusian and Foreign Mathematical Centers:** Belarusian State University, Mathematical Institute of Belarusian National Academy of Sciences, Moscow State University, Steklov Mathematical Institute of Russian Academy of Sciences, Space Research Institute of Ukraine National Academy of Sciences, Ecole Centrale des Nantes (France), Institute of Mathematics of Polish Academy of Sciences, Banach International Mathematical Center (Poland), Warsaw University of Technology, University of Minnesota (USA), TAMU (USA), Holon Institute of Technology (Israel) and others

**RESEACH ACTIVITY AND RESULTS**

The research activity is concerned with mathematical methods and models for the qualitative control and observations theory for complex dynamical systems with after-effect. The main achievements in this field are the following: *development of an algebraic approach to solving the relative controllability problem for linear dynamical systems with retarded argument* (1971-1976); *solution of the problem of Krasovskii of complete controllability (total quieting) of linear dynamical systems with time delay* (1977); *statements and mathematical methods for the solution of the modal control problem (pole assignment) for difference-differential control systems both with complete and incomplete state information* (1976-1981) and for *functional-differential systems with distributed delay* (1990-1993); *mathematical methods and criteria for pointwise (multipoint) controllability and observability of linear difference-differential systems and relation to controllability and observability of one-parametric systems without delay* (1978-1989); *canonical representations for linear dynamical systems with retarded argument* (1978-1984, 1988-1990); *development of the general minimal state approach to the investigation of the problem of controllability and observability for general functional-differential systems of neutral type* (1984-1986); *feedback control* (stabilization, modal control, classification, reconstruction and others*) for several classes of controlled systems by using various kinds of feedback controllers such as difference controllers, integral ones and others* (1991-1998); *mathematical problems of realization of time-delay systems* (1999-on);*hybrid systems: *solution representations, controllability, observability, duality, stability and stabilization (1999-on); *observability of nonlinear systems *(2000-on); *scale realization of dynamical systems with after-effect* (2002-on); *discrete-continuous hybrid dynamical systems*: *stability, stabilization, controllability, reachability, observability, duality *(2012-on).* *It should be noted that the main mathematical* *methods used to solve the problems above can be successfully applied* *to other more general classes of dynamical systems, in particular,* *to descriptor and hybrid systems and to systems with* “*multidimensional” time (2-D Systems).