The research work of S. G. Tzafestas is broadly divided in two large periods. The first period starts from the time of his Ph.D. studies (1966-68), and involves his engagement as a research leader in the Department of Computers of the Nuclear Research Centre 'Demokritos', Athens (1969-72), and as a Systems and Control Professor in the Electrical Engineering Department of Patras University, Patras, Greece (1973-84).

The research areas covered in this period are:

- Distributed parameter systems
Distributed Parameter Systems (DPS)
The main contributions in the DPS area concern the optimal control of nonlinear DPS. He has derived optimal control algorithms and policies using differential dynamic programming, maximum principle, variational calculus, and functional analysis. Another topic where he has made a substantial contribution is the nonlinear filtering of DPS. His results were derived using the maximum likelihood, the Fokker-Planck equation, and the least-squares methodologies. He has applied his results to the control of space-dependent nuclear reactors, flexible-link robots, and to the gamma ray imaging problem. Other important contributions concern the filtering, identification, smoothing, hybrid simulation, stochastic control, adaptive control, and eigenvalue control problems. In the DPS area he has also published several comprehensive survey papers and book chapters, and the following edited research book:
**Distributed Parameter Systems: Theory and Application**,*Pergamon Press*(1982).#### Key Publications

- Optimal filtering, smoothing and prediction in linear DPS,
*Proc.IEE*, Vol.115, No.8, pp.207-1212 (1968). - Differential dynamic programming approach to optimal nonlinear DPS,
*Proc.IEE*, Vol.116, No.6, pp.1078-1084 (1969). - Maximum likelihood approach to the optimal filtering of DPS,
*Proc.IEE*, Vol.116, No.6, pp.1078-1093 (1969). - Optimal DP control using classical variational theory,
*Intl. J.Control*, Vol.12, No.4, pp.593-608 (1970). - Distributed-parameter control in function space,
*J.Franklin Inst.*, Vol.295, No.4, pp.317-342 (1973). - Nonlinear distributed-parameter filtering using the Fokker-Planck equation,
*J.Franklin Inst.*, Vol.301, No.5, pp.429-449 (1976). - Stochastic distributed filtering approach to gamma ray imaging,
*Int. J.Systems Sci.*, Vol.7, No.11, pp.1249-1274 (1974). - Distributed-parameter optimal control via mathematical programming,
*J.Franklin Inst.*, Vol.309, No.6, pp.399-438 (1980). - Singularly perturbed large-scale DPS: An application to nuclear reactor control,
*Maths & Computers in Simul.*, Vol.24, pp.303-313 (1982). - Dynamic studies of flexible robot manipulators, In:
*Distributed-Parameter Systems: Modeling and Simulation*(T.Futagami et.al.eds), North-Holland, pp.321-344 (1989). - Robustness of a special assignment method applied to a flexible beam,
*Int.J.Control*, Vol.70, No.6, pp.859-872 (1998). - Adaptive control of flexible joint robots via the singular perturbation approach,
*Syst. Anal.Modell. Simul.*, Vol.38, No.2, pp.477-494 (2000). - Control of flexible joint robots using neural networks,
*IMA J. Mathem-Control and Information*, Vol.18, pp.269-280 (2001).

- Optimal filtering, smoothing and prediction in linear DPS,
- Computing, buffering, hardware, and microprocessor-based systems
The work in this area belongs mainly to the first period of research and development efforts (1969-1985). It concerns the study, analysis and design of electronic buffering systems, software and hardware computational systems, and μP- based systems. The particular topics considered include: logic design of computer buffer memories, statistical design of buffering systems using finite-length queuing theory; computational algorithms for system simulation, optimization and direct digital control; human-computer and plant-computer interactive systems, hardware design of stochastic computers, design and implementation of PFM and PWM control systems, microprogramming design and simulation of mini-control computers, microprocessor-based implementation of digital controllers and simulators, and digital filter design based on logarithmic processing. Currently, work is performed on the VLSI design and implementation of fast digital fuzzy logic controllers (DFLCs) using FPGA (field programmable gate array) devices. In this area he has published the following contributed books:
**Microprocessors in Signal Processing, Measurement and Control**,*D. Reidel Dordrecht*(1983).**Methods and Applications in Measurement and Control**,*ACTA Press*, Calgary (1984).**Digital Techniques in Simulation, Communication and Control**,*North-Holland*, Amsterdam (1985).**Real-Time Microcomputer Control of Industrial Processes**,*Kluwer*, Boston-Dordrecht (1990).

#### Key Publications

- On the design of electronic buffer memories,
*Proc.Intl. Symp. on Logical Design and Applications, U.L.B. Publications*, Brussels, pp.1061-1074, Sept.(1969). - Variable digital design for P+I Controller,
*Control & Instrumentation*, pp.45-47, July/August (1971). - On buffer design for Erlang arrivals and multiple periodically regular outputs,
*Intl.J. Systems Science*, Vol.2, No.4, pp.353-367 (1972). - Digital control of motor speeds avoids discontinuities,
*Control Engrg.*, pp.53-55, July (1974). - Analysis and design of multi-input/multi-priority buffering systems with binomial feedback,
*J.Franklin Inst*, Vol.302, No.1, pp.19-36, July (1976). - Implementing PFM controllers,
*Electronic Engrg.*, pp.91-104, Nov.(1979). - Design and implementation of pulse frequency modulation control systems,
*Trans.Institute Meas.& Control*, Vol.13, No.2, pp.65-78 (1980). - Design and simulation of a mini control computer,
*Found Control Engrg.*, Vol.7, pp.53-63 (1982). - Digital controllers and their microprocessor-based implementation, In:
*μPs in Signal Processing Measurement & Control*, D.Reidel, pp.231-279 (1983). - Human-computer interfaces: Artificial intelligence and software psychology issues,
*Proc. Europ. Conf. on Geographical Information Systems (EGIS '90)*, Amsterdam, April (1990). - Design and implementation of a fast digital fuzzy logic controller using FPGA technology,
*J.Intell. and Robotic Systems*, Vol.45, No.1, pp.77-96 (2006). - A parameterized T-S digital fuzzy logic processor: Soft core VLSI design and FPGA implementation,
*J.of Factory Autom., Robotics and Soft Comp.*(2006).

- Multivariable systems
The work in this field includes linear continuous- time and discrete-time systems, as well as bilinear, nonlinear, time-delay, and finite-state systems (sequential machines/ automata). The work in this area has started early in his career (1972) and is continued until now. The problems considered were tackled by highly original methods, and include the following: input-output modeling, identification, optimization, sensitivity analysis, input-output decoupling, state observer design, state estimation, model matching, eigenvalue (modal) control, model-based predictive control, hierarchical control, adaptive control, and multivariable robust stabilization and control. Some of the results have been applied to nuclear reactors, production/ inventory systems, and solar energy systems. Again, in the MVS area he has published important survey papers, and the following three contributed reference books:
**Multivariable Control: Concept and Tools**,*D.Reidel*(1984).**Applied Digital Control**,*North-Holland*(1985).**Applied Control: Recent Trends and Applications**,*Marcel Dekker*(1993).

#### Key Publications

- Input-output modeling and identification of linear automata,
*Inform. Processing Letters*, Vol.1, No.3, pp.69-75 (1972). - Multivariable control theory of linear sequential machines,
*Intl.J.Systems Science*, Vol.4, No.3, pp.363-396 (1973). - Eigenvalue controller design of reduced sensitivity,
*Proc.IEEE*, Vol.63, No.1, pp.1080-1081 (1975). - Model matching multicontroller design of reduced sensitivity,
*Autom Control Theory & Appl.*, Vol.3, pp.57-69 (1975). - Partial decoupling in a class of nonlinear control systems,
*Electron Lett*, Vol.12, No.6, pp.145-147 (1976). - Multivariable control system identification using pseudorandom inputs,
*Autom.Control Theory and Applications*, Vol.5, Sept (1977). - Stabilizing optimal control of bilinear systems with a generalized cost,
*Optimal Contr. Theory and Methods (OCAM)*, Vol.5, pp.111-117 (1984). - New computationally efficient formula for backward pass fixed-interval smoother and its U-D factorization algorithm,
*Proc.IEE*, Vol.136 (Part D), No.2, pp.73-78 (1989). - A hierarchical multiple model adaptive control of discrete-time stochastic systems for sensor and actuator uncertainties,
*Automatica*, Vol.26, pp.875-886 (1990). - PID self-tuning control combining pole placement and parameter optimization,
*Math & Computers in Siml.*, Vol.37, pp.133-142 (1994). - A unified hierarchical control algorithm for constrained nonlinear multi-delay interconnected systems:
*Application to production planning, Control-Theory and Advanced Technology (C-TAT)*, Vol.10, No.4 (Part 4), pp.1737-1761 (1995). - Stability robustness of feedback linearizable systems with input unmodeled dynamics,
*IEE Proc.-Control Theory Appl.*, Vol.146, pp.77-83 (1999). - A small gain theorem for locally input-to-state stable interconnected systems,
*J.Franklin Inst*, Vol.336, pp.893-901 (1999).

- Multidimensional systems
Multidimensional (m-D) Systems
The work in the m-D systems area has started in 1981 and was extended until the end of 90's. Important original results have been derived for the following problems: State-space modeling, transfer function modeling, factorization, state reconstruction, characteristic polynomial assignment, state feedback control, model matching, stability analysis, and stabilizing control. His 3-D (and m-D) state-space model represents a major contribution and constitutes one of the alternative models extensively used in the field. Some of the results have been applied to 3-D image restoration and control of DPS. His work includes comprehensive surveys and the following seminal reference book:
**Multidimensional Systems: Techniques and Applications**,*Marcel Dekker*, N.Y. (1986).#### Key Publications

- Exact model-matching control of 3-D systems using state and output feedback,
*Intl.J.Syst. Science*, Vol.13, No.11, pp.1171-1187 (1982). - Characteristic polynomial assignment of 3-D discrete systems using a canonical state space model,
*Intl. J. Syst. Science*, Vol.15, No.2, pp.175-186 (1984). - Reducibility and factorizability of multivariable polynomials,
*Control: Theory and Advanced Technology*, Vol.1, No.1, pp.25-46 (1985). - Open loop dead-beat control of m-D systems,
*J.Franklin Inst*, Vol.329, No.3, pp.311-324 (1985). - Parallel Kalman filter bank design for adaptive image restoration,
*In: Parallel Processing Techniques for Simulation (M.Singh et al., eds), Plenum*, pp.217-228 (1986). - An inductive approach to the state space representation of m-D systems,
*Control: Theory and Advanced Technology (C-TAT)*, Vol.3, pp.293-322 (1987). - A new stability test for 2-D discrete systems using bilinear continued fractions,
*IEEE Trans. Circuits & Systems*, Vol.CAS-36, No.1, pp.141-144 (1989). - Stability tests for 2-D systems using the Schwarz form and inners determinants,
*IEEE Trans. Circuits & Systems*, Vol.CAS-38, pp.1071-1077 (1991). - Two dimensional digital filters without overflow oscillations and instability due to finite word length,
*IEEE Trans.on Signal Processing*, Vol.40, No.9, pp.2311-2317 (1992). - A general factorization method for multivariable polynomials,
*Multid. Systems and Signal Processing*, Vol.5, pp.151-178 (1994). - Stability margin of 2-dimensional discrete systems,
*Syst. Anal. Modell Simul.*, Vol.15, pp.159-173 (1994). - Non-standard state-space models for 2D systems,
*Bull.Polish Acad. Sciences*, Vol.47, No.1, pp.91-101 (1999).

- Exact model-matching control of 3-D systems using state and output feedback,
- Nuclear reactor systems
Nuclear Reactor Systems (NRS)
This is an application area in which S.G.Tzafestas has been engaged during his service as a research leader and later as a research fellow (1969-85; simultaneously to his Professorial position in Patras) in the Nuclear Research Center "Democritus" (Athens). His research in this area includes practical work with PID industrial control, and applied theoretical work on the following topics: digital modeling of NRS, identification of NRS, multivariable control of NRS, optimal control of distributed-parameter NRS, decoupling control of NRS, Walsh function, and variational synthesis of NRS. He has also done R&D work concerning the reliability and safety of power reactors.
#### Key Publications

- On the digital-model design for nuclear reactor computation and control,
*Nuclear Instruments and Methods*, Vol.84, pp.207-210 (1970). - Distributed-parameter nuclear reactor optimal control, In:
*New Trends in Systems Analysis (J.L.Lions and A.Bensoussan, eds), INRIA Publications, France*, pp.33-62 (1976); Also: Springer Series on Control and Information Sciences (1977). - Canonical decoupling and control of multi-core nuclear reactors,
*Nuclear Science & Engrg.*, Vol.62, pp.574-579 (1977). - Time-varying reactivity reconstruction via Walsh functions,
*IEEE Trans. Auto Control*, Vol.AC-22, pp.885-888 (1977). - Test inputs for nuclear reactor indentification,
*Autom.Control Theory & Appl.*, Vol.5, Sept. (1977). - Control of nuclear reactors using Walsh function variational synthesis,
*Nuclear Science & Engrg.*, Vol.62, pp.763-770 (1977). - Automatic control, reliability, and safety of nuclear power reactors,
*First National Symp. on Peaceful Applications of Nuclear Energy, Greek Atomic Energy Commission*, Athens (1979). - Control of nuclear power plants,
*Autom. Control Theory & Appl.*, Vol.8, No.3, pp.37-50 (1980). - Dynamic reactivity computation in nuclear reactors using block-pulse function expansion,
*Intl. J. Modelling and Simul.*, Vol.4, No.2, pp.73-76 (1984). - Application of an exact model matching technique to coupled-core nuclear reactor control,
*Nuclear Science & Engrg.*, Vol.87, pp.454-495 (1984).

- On the digital-model design for nuclear reactor computation and control,
- Walsh expansion-based system analysis and control
During the period 1976-1997 S.G.Tzafestas has developed several systems analysis and control techniques using Walsh and block-pulse function expansions. The topics covered include: Walsh function hardware generator design, system input-output analysis, system identification, observer and optimal filter design, hardware Walsh function analyzer design, optimal control, treatment of distributed-parameter and time-delay systems, system design for data compression. The applications include nuclear reactor systems, electrocardiogram (ECG) signal processing, and DPS. His work in this important area includes the publication of the following book which contains in reprinted form 38 seminal papers published by the year 1985:
**Walsh Functions in Signal and System Analysis and Design**,*Van Norstand Reinhold*, N.Y. (1985).#### Key Publications

- Global Walsh function generators,
*Electronic Engrg.*, pp.45-49, July (1976). - Walsh series approach to observer and filter design in optimal control systems,
*Intl.J.Control*, Vol.26, pp.721-735 (1977). - Walsh series approach to lumped and distributed system identification,
*J.Franklin Inst.*, Vol.305, No.4, pp.199-220 (1978). - Walsh series approach to time delay control system observer design,
*Intl.J.Systems Sci.*, Vol.9, No.3, pp.287-299 (1978). - A digital Walsh function analyzer,
*Electronic Engrg.*, pp.91-104, Nov. (1979). - A fast digital Walsh-Hadamard signal processing system,
*Maths.& Computers in Simul.*, Vol.23, No.2, pp.206-212 (1981). - Walsh transform theory and its application to system analysis and control,
*Maths.& Computers in Simul.*, Vol.25, pp.214-225 (1983). - Walsh and block-pulse operational matrices in distributed-parameter and delay systems, In:
*Digital Techniques in Simulation, Communication and Control*(S.Tzafestas, Ed), pp.27-34, North-Holland (1984). - A fast Walsh-transform-based data compression multi-microprocessor system: Application to ECG signals,
*Maths.& Computers in Simul.*,Vol.27, pp.491-502 (1985). - New results on Walsh function analysis and identification of DPS, In:
*Complex and Distributed Systems: Analysis Simulation and Control*, pp.251-262, North-Holland (1986). - Walsh function analysis of parabolic DPS with time-and space- varying parameters,
*Found. Comp. Decision Sci.*, Vol.22, No.3, pp.185-194 (1997).

- Global Walsh function generators,