Research History
Michael Sebek started his research career as a disciple of Vladimir Kucera.
Current Research
Current research interests of Michael Sebek include:
In early 1980s, Michael Sebek contributed to polynomial control theory. He found polynomial equation solutions of various special control problems for multi-input multi-output systems such as signal tracking, exact model matching and deadbeat control.
In late 1980s, Michael Sebek pioneered the 2-D and n-D polynomial equation approach to control system and filter design for the class of complex systems and processes (delay-differential systems, 2-D and n-D systems, multi-pass processes, repetitive systems, systems described by partial differential equations, etc.) that are described by two or more different type of operators (integrators and time-delays, temporal and/or spatial shifts in various directions, etc.). For such systems, standard 1-D polynomial equations must be replaced by equations with polynomials and polynomial matrices in two or more different indeterminates. Michael Sebek introduced the 2-D and n-D polynomial equations, developed both theory and computational algorithms and applied them to solve various control problems. Since then, the equations have also appeared useful in other areas of engineering such as robust control design, and 2-D signal processing.
In early 1990s, Michael Sebek contributed to robust control design via polynomial matrices. He investigated the theory of
J-spectral factorization of polynomial matrices and co-authored first computational algorithms. Due to its indefinite nature, the factorization is both theoretically appealing and practically important. It is an important step in the design of robust H-infinity optimal and
sub-optimal controllers via polynomial approach, which is equivalent to an indefinite algebraic Riccati equation. He also contributed to robust analysis and design of systems with parametric uncertainties.
In mid 1990s, Michael Sebek developed the next generation of numerical algorithms for operations and equations with polynomial matrices that are numerically more reliable then classical ones. They are based on interpolation and Sylvester matrix approach. He authored and co-authored numerous new reliable and efficient routines for various special polynomial matrix equations. He co-authored first numerically stable procedures for triangularization, greatest divisors and rank evaluation of polynomial matrices etc.
In late 1990s, Michael Sebek developed the third generation of numerical methods for polynomial matrices
and contributed to the application of Linear Matrix Inequalities (LMI's) for polynomial matrices to be particularly used for robust control of plants with parametric uncertainties. The third generation of numerical routines for polynomial matrices is extremely fast as it is based on Fast Fourier Transform. Michael proposed this research direction and co-authored pioneering papers on new determinant computation for polynomial matrices and a new spectral factorization method.
The LMI's became an important tool in state space based control theory. Michael co-authored first papers using LMI's for polynomial methods.
Michael Sebek co-authored Polynomial Toolbox, the MATLABTM toolbox for polynomials, polynomial matrices and their applications in systems, signals and control. The Toolbox enables to apply the polynomial methods in industry.
Its first version - Polynomial Toolbox 1.5 for MATLAB 4 - was a very successful freeware package downloaded and used by more than 1.000 users
(including major industrial companies such as Kodak, DaimlerChrysler, Boeing, Motorola, Ericsson and others).
The current version - Polynomial Toolbox 2.5 for MATLAB 6 - is object oriented and hence more user friendly; based on new algorithms and hence much faster; includes numerous new functions and design methods; handles also complex coefficients and hence is better suited for signal processing.
It is commercially available through PolyX Ltd., Prague at www.polyx.com and www.polyx.cz.