The research interests of V. Kučera are in linear systems and control theory.
In the early 1970s, V. Kučera contributed to the theory of matrix Riccati equations. He found necessary and sufficient conditions for the existence of extremal, nonnegative definite, steady-state solutions of these equations in terms of stabilizability and detectability. Further, he classified the set of all nonnegative definite steady-state solutions and showed that the set is a lattice. These results are fundamental for the design of linear-quadratic optimal control systems.
Kučera V.: A contribution to matrix quadratic equations. IEEE Transactions on Automatic Control AC-17 (1972), 3, 344-347.
Kučera V.: On nonnegative definite solutions to matrix quadratic equations. Automatica 8 (1972), 4, 413-423.
Kučera V.: Algebraic Riccati equation: Hermitian and definite solutions. The Riccati Equation (S. Bittanti, A. J. Laub and J.C. Willems, Eds.). Springer, Berlin 1991, 53-88.
In the late 1970s, he proposed new control strategies for discrete-time linear systems, in which the control process is settled in the shortest possible time for every initial state of the system. The synthesis of the controls is done both in the time domain and in the frequency domain. The results have been applied in the design of fast and precise servomechanisms.
Kučera V.: A dead-beat servo problem. Int. J. Control 32 (1980), 1, 107-113.
Kucera V., Šebek M.: On deadbeat controllers. IEEE Trans. Automatic Control AC-29 (1984), 8, 719-722.
Kucera V.: Deadbeat control, pole placement, and LQ regulation. Kybernetika 35 (1999), 6, 681-692.
V. Kučera pioneered a new approach to synthesizing linear control systems, known as the polynomial equation approach. In this approach, the transfer function of the plant is represented in a fractional form. Any and all controllers that meet the design specifications are then obtained by solving linear polynomial diophantine equations. The polynomial equation approach found followers worldwide and inspired efficient computational algorithms for polynomials and polynomial matrices. This approach also paved the way for a parametrization of all stabilizing controllers.
Kučera V.: Design of steady-state minimum variance controllers. Automatica 15 (1979), 4, 411-418.
Kučera V.: New results in state estimation and regulation. Automatica 17 (1981), 5, 745-748.
Kučera V.: Diophantine equations in control - a survey. Automatica 29 (1993), 6, 1361-1375.
The best-known result of V. Kučera is the parameterization of all controllers that stabilize a given system, frequently referred to as the Youla-Kučera parameterization. It was obtained independently and at about the same time by D.C. Youla and V. Kučera. The parameterization formula is due to V. Kučera, whereas the use of the parameter in H2 optimal control is due to D.C. Youla. The parameterization result launched an entirely new area of research with applications in optimal and robust control.
Kučera V.: Stability of discrete linear feedback systems. Preprints 6th IFAC Congress, Boston 1975, Vol. 1, Paper 44.1.
Kučera V.: Discrete Linear Control: The Polynomial Equation Approach. Wiley, Chichester 1979.
Kučera V.: Polynomial control: past, present, and future. International Journal of Robust and Nonlinear Control 17 (2007), 8, 682-705.
In the 1980s, V. Kučera contributed to the theory of linear control systems whose behavior is described by a system of implicit differential equations. He found the limits of state variable feedback in altering the dynamics of such systems, identified the dynamic precompensation that can be realized using static state feedback around the system, and solved the H2 control problem for this general control system configuration.
Kučera V., Zagalak P.: Fundamental theorem of state feedback for singular systems. Automatica 24 (1988), 5, 653-658.
Kučera V.: Stationary LQG control of singular systems. IEEE Transactions on Automatic Control AC-31 (1986), 1, 31-39.
Kučera V., Herrera Hernandez A.N.: Static realization of dynamic precompensators for descriptor systems. Systems & Control Letters 16 (1991), 4, 273-276.
The main research interests of V. Kučera in the 1990s included optimal and robust control. He proposed several algorithms for H2 optimization of control systems and developed a simple approximate solution of robust control design via pole placement techniques. He obtained several necessary and sufficient conditions for system stabilization using static output feedback.
Kučera V., Kraus F. J.: Regional pole placement. Kybernetika 31 (1995), 6, 541-546.
Trofino Neto A., V. Kučera: Stabilization via static output feedback. IEEE Transactions on Automatic Control AC-38 (1993), 5, 764-765.
Kučera V., de Souza C. E.: A necessary and sufficient condition for output feedback stabilizability. Automatica 31 (1995), 9, 1357-1359.
In the first decade of this millennium, V. Kučera continued research into robust stability and performance using polynomial methods. He applied Youla-Kučera parameterization to stabilize linear systems subject to input constraints, to achieve the desired input and output shaping, including overshoot reduction, and to design fixed-order stabilizing controllers in linear time-invariant systems. He obtained a general transfer-function solution of the H2 control problem and compared this solution with the state-space design algorithm.
Henrion D., Tarbouriech S., Kučera V.: Control of linear systems subject to input constraints: a polynomial aproach. Automatica 37 (2001), 4, 597-604.
Henrion D., Kučera V., Molina-Cristobal A.: Optimizing simultaneously over the numerator and denominator polynomials in the Youla-Kučera parametrization. IEEE Transactions on Automatic Control 50 (2005), 9, 1369-1374.
Gadewadikar J., Lewis F.L., Xie L., Kučera V., Abu-Khalaf M.: Parametrization of all stabilizing H inf static state-feedback gains: Application to output-feedback design. Automatica 43 (2007), 9, 1597-1604.
In the following decade, V. Kučera investigated model matching, decoupling, and stabilization of linear systems by nonregular state feedback. He has resolved a long-standing open problem of linear systems theory, the decoupling by static-state feedback. The earliest known investigation of system decoupling dates back to 1934, a rigorous state space formulation of the problem appeared in 1964, and a solution for square and invertible systems followed in 1967. The general case of right-invertible systems and nonregular static-state feedback compensation, however, has withstood all past efforts to obtain a solution.
Kučera V.: Stable model matching by non-regular static state feedback. IEEE Transactions on Automatic Control 61 (2016), 12, 4138 - 4142.
Kučera V.: Diagonal decoupling of linear systems by static-state feedback. IEEE Transactions on Automatic Control 62 (2017), 12, 6250 - 6265.
Kučera V.: Block decoupling of linear systems by static-state feedback. IEEE Transactions on Automatic Control 64 (2019), 8, 3447-3452.
In the twenties, V. Kučera discovered the canonical form and the complete invariant of stable linear systems with respect to the group of transformations which consists of stability-preserving state feedback, stability-preserving output injection, and the change of bases in the input, output, and state spaces. This result facilitated the general solution to the famous problem of decoupling a linear system while maintaining stability. Further, he developed an algebraic solution for modifying infinite zero orders in linear multivariable systems using (nonregular) state feedback and showed that the set of assignable orders is a lattice.
Kučera V.: Stability-preserving Morse normal form. IEEE Transactions on Automatic Control 65 (2020), 12, 5099-5113.
Kučera V.: Decoupling with stability of linear systems by static-state feedback. IEEE Transactions on Automatic Control 66 (2021), 10, 4684-4699.
Kučera V.: Assignment of infinite zero orders in linear systems using state feedback. Automatica 135 (2022),
V. Kučera was invited to deliver plenary lectures at prestigious conferences, including the
- 42nd IEEE Conference on Decision and Control 2003 (Feedback Control: the Origins, the Milestones, and the Trends),
- 1st European Control Conference 1991 (Diophantine Equations in Control),
- XII. Congresso Brasileiro de Automática 1998 (Three Approaches to H2 Control Theory),
- 8th IFAC Symposium on Robust Control 2015 (Control Theory and Its Impact on Society),
- Joint 7th IFAC Symposium on System Structure and Control 2019 and 15th IFAC Workshop on Time Delay Systems 2019 (Decoupling. A Long-Standing Open Problem Resolved),
- 21st International Conference on Informatics in Control, Automation and Robotics 2024 (Youla-Kučera parameterization: Theory and Applications).
V. Kučera has had the pleasure and privilege of working with many researchers worldwide, including
- CZ: M. Šebek, P. Zagalak, J. Ježek, S. Čelikovský, P. Zítek, T. Vyhlídal, M. Hromčík, J. Cigler, P. Hušek, Z. Vostrý, V. Strejc, J. Beneš, M. Kárný, P. Černý, J. Vacík, P. Kovanic, J. Šindelář, J.V. Outrata, M. Krupička
- SK: P. Brunovský, V. Veselý, D. Rosinová, M. Fikar, A. Kozáková, J. Paulusová
- FR: D. Henrion, M. Malabre, S. Tarbouriech, J.F. Lafay, J.J. Loiseau, J. Descusse, P. Picard, Ph. de Larminat
- MX: J.C. Martínez García, L.E. Ramos Velasco, S. Mondié, J. Ruiz León, A.N. Herrera Hernandez, G. Fernández Anaya, D. Aguilar George, V. Lopez Morales, A. Molina Cristobal, M.A. Bernal Reza, J.J. Flores Godoy, R. Galindo, J.J. Leyva Montiel, E. Castañeda Toledo
- IT: P. Colaneri, S. Bittanti, S. Longhi
- BE: J.L.Willems, M. Gevers, V. Blondel
- SE: K.J. Åström, T. Söderström, A. Lindquist
- US: F.L. Lewis, J. Hench, V. Syrmos, J. Gadewadikar, L. Xie, M. Abu-Khalaf
- CH: F. Kraus, M. Mansour, W. Schaufelberger
- UK: M. Grimble, K.J.Hunt
- AU: B.D.O. Anderson
- TR: K. Özçaldıran, V. Eldem
- JP: K. Furuta
- BR: C.E. de Souza, A. Trofino Neto
- DE: H. Werner, H.-J. Koriath, M. Hoffmann, U. Priber, V. Mehrmann, C. He
- GR: P.P. Groumpos, F.N. Koumboulis
- CN: X. Liu
- EG: M.M. Anis Ismail
- VN: M.H. Hoang
- UA: T. Korotka
Research Projects
Following is the record of the recent research projects of which V. Kučera was (or still is) the Principal or Associated Investigator. In addition, he participated in many other projects of research and education. The total support of these projects exceeds 1,150 M CZK.
- Linear Control Theory: An Algebraic Approach
Grant Agency of the Czechoslovak Academy of Sciences: 27501
Contractor: Institute of Information Theory and Automation
Period: 1991-1992 - Linear Control Systems Design: A Fractional Representation Approach
Grant Agency of the Academy of Sciences of the Czech Republic: A 275102
Contractor: Institute of Information Theory and Automation
Period: 1993-1995 - Methods and Algoritmus for Robust Control
Grant Agency of the Czech Republic: 102/94/0294
Contractor: Institute of Information Theory and Automation
Period: 1994-1996 - Structure of Linear Systems
Tubitak-Doprog Turkey
Contractor: Marmara Research Center
Period: 1994-1998 - Structure des systemes lineaires, a retards et instationnaires
Centre National de la Recherche Scientifique: 1622
Contractor: Academy of Sciences of the Czech Republic
Period: 1995-1997 - Dynamic Control & Management Systems in Manufacturing Processes
European Commission: CP94-1246
Contractor: University of Strathclyde
Period: 1995-1998 - Tools and Methods of Computer Science, Cybernetics and Information Transmission
Academy of Sciences of the Czech Republic: K1-075-601
Contractor: Institute of Information Theory and Automation
Period: 1996-2000 - Robust Control Systems Design
Grant Agency of the Czech Republic: 102/97/0861
Contractor: Institute of Information Theory and Automation
Period: 1997-1999 - Advanced Methodologies and Tools for Manufacturing Systems
European Commission: CP96-0026
Contractor: University of Patras
Period: 1997-2000 - Intelligent Systems of Scientific Data Transmission and Processing
Academy of Sciences of the Czech Republic: P1-075-701
Contractor: Institute of Information Theory and Automation
Period: 1997-1999 - Trnka Laboratory for Autonomic Control
Ministry of Education of the Czech Republic: VS97034
Contractor: Czech Technical University in Prague
Period: 1997-2000 - Control Engineering Education and Research
Schweizerischer Nationalfonds: 7 IP 51791
Contractor: ETH Zuerich
Period: 1997-1998 - Robustesse et structure des systemes lineaires sur anneuax
Centre National de la Recherche Scientifique: 5108
Contractor: Academy of Sciences of the Czech Republic
Period: 1998-2000 - Robust Control Systems Design
Ministry of Education of the Czech Republic: NJ-05
Contractor: Czech Technical University in Prague
Period: 1998-2000 - Information Point for the European IST Prize
Ministry of Education of the Czech Republic: OK 318
Contractor: Academy of Engineering of the Czech Republic
Period: 1998-2000, 2001-2005 - The European Network for Industrial Application of Polynomial Design Methods
European Commission: CP97-7010
Contractor: Institute of Information Theory and Automation
Period: 1998-2001 - Dynamic Control & Management Systems in Manufacturing Processes (Phase 2)
European Commission: CP97-7022
Contractor: University of Strathclyde
Period: 1998-2001 - Periodic Discrete-Time Systems
Ministry of Education of the Czech Republic: 28/61
Contractor: Czech Technical University in Prague
Period: 1998-2001 - Center for Applied Cybernetics
Ministry of Education of the Czech Republic: LN00B096
Contractor: Czech Technical University in Prague
Period: 2000-2004 - TALENT – coordinated education of Ph.D. students in control engineering and robotics
Grant Agency of the Czech Republic: 102/03/H116
Contractor: Czech Technical University in Prague
Period: 2003-2006 - Information Point for the European IST Prize
Ministry of Education of the Czech Republic: OK 466
Contractor: Academy of Engineering of the Czech Republic
Period: 2006-2007 - Center for Applied Cybernetics 2
Ministry of Education of the Czech Republic: 1M0567
Contractor: Czech Technical University in Prague
Period: 2005-2011 - Self-Learning Sheet Metal Forming System – LearnForm
European Commission: NMP2-SL-2009-228346
Coordinator: Fraunhofer IWU Chemnitz
Period: 2009-2012 - Self-Learning Sheet Metal Forming System – LearnForm
Ministry of Education of the Czech Republic: 7E09094
Contractor: Czech Technical University in Prague
Period: 2009-2012 - Identification of Stochastic, Nonlinear Systems for Advanced Control
Grant Agency of the Czech Republic: GA103/12/1187
Contractor: Czech Technical University in Prague
Period: 2012-2014 - Center for Applied Cybernetics 3
Technology Agency of the Czech Republic: TE01020197
Contractor: Czech Technical University in Prague
Period: 2012-2019 - Time-Delay Compensators for Flexible Systems
Grant Agency of the Czech Republic: GA16-17398S
Contractor: Czech Technical University in Prague
Period: 2016-2018 - Draft prospects of the thematic areas of research, development, and innovation, responding to the context, content, and scope of the so-called fourth industrial revolution (Industry 4.0)
Technology Agency of the Czech Republic: TB095TACR999
Contractor: Czech Technical University in Prague
Period: 2016-2016 - Complex systems for scheduling, planning, and control, National Competence Center – Cybernetics and Artificial Intelligence Technology Agency of the Czech Republic: TN01000024/01
Contractor: Czech Technical University in Prague
Period: 2019-2022