Vasile Mihai Popov (born 1928) is a leading

systems theorist Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structu ...

and

control engineering Control engineering or control systems engineering is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls o ...

specialist. He is well known for having developed a method to analyze

stability Stability may refer to: Mathematics *Stability theory, the study of the stability of solutions to differential equations and dynamical systems ** Asymptotic stability ** Linear stability ** Lyapunov stability ** Orbital stability ** Structural sta ...

of nonlinear

dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a p ...

, now known as Popov criterion.

Biography

He was born in Galaţi, Romania on July 7, 1928. He received the engineering degree in electronics from the

Bucharest Bucharest ( , ; ro, București ) is the capital and largest city of Romania, as well as its cultural, industrial, and financial centre. It is located in the southeast of the country, on the banks of the Dâmbovița River, less than north of ...

Polytechnic Institute An institute of technology (also referred to as: technological university, technical university, university of technology, technological educational institute, technical college, polytechnic university or just polytechnic) is an institution of te ...

in 1950. He worked for a few years as Assistant Professor at the Bucharest Polytechnic Institute in the Faculty of Electronics. His main research interests during this period were in frequency modulation and parametric oscillations. In the mid 1950s, he joined the Institute for Energy of Romanian Academy of Science in Bucharest. In the 1960s, Popov headed the Control group at the Institute of Energy of the

Romanian Academy The Romanian Academy ( ro, Academia Română ) is a cultural forum founded in Bucharest, Romania, in 1866. It covers the scientific, artistic and literary domains. The academy has 181 active members who are elected for life. According to its byl ...

. In 1968 Popov left Romania. He was a visiting professor at the Electrical Engineering departments of

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

, and

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

, and then Professor in the department of electrical engineering at the

University of Maryland College Park The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland. Founded in 1856, UMD is the flagship institution of the University System of Mary ...

. In 1975 he joined the mathematics department of

University of Florida The University of Florida (Florida or UF) is a public land-grant research university in Gainesville, Florida. It is a senior member of the State University System of Florida, traces its origins to 1853, and has operated continuously on its ...

Gainesville. He retired in 1993 and currently resides in

Gainesville, Florida Gainesville is the county seat of Alachua County, Florida, Alachua County, Florida, and the largest city in North Central Florida, with a population of 141,085 in 2020. It is the principal city of the Gainesville metropolitan area, Florida, Gaine ...

, USA.

Work

Qualitative theory of differential equations

Motivated by stability issues in nuclear reactors and by his participation in a seminar series on

qualitative theory of differential equations In mathematics, the qualitative theory of differential equations studies the behavior of differential equations by means other than finding their solutions. It originated from the works of Henri Poincaré and Aleksandr Lyapunov. There are relatively ...

run by A. Halanay, Popov started working in stability of nonlinear

feedback Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handled ...

systems, in particular on the Lur'e-Postnikov problem. In 1958/59 he obtained, through a very original approach, the first frequency stability criterion for a class of nonlinear feedback control systems. He continued this work and obtained the equivalence between the

state space A state space is the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory. For instance, the toy ...

(

Lyapunov function In the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Lyapunov functions (also called Lyapunov’s se ...

based) approach and the frequency domain approach for stability and obtained a very perceptive characterization of

passive Passive may refer to: * Passive voice, a grammatical voice common in many languages, see also Pseudopassive * Passive language, a language from which an interpreter works * Passivity (behavior), the condition of submitting to the influence of o ...

systems, nowadays known as the celebrated

Kalman–Yakubovich–Popov lemma The Kalman–Yakubovich–Popov lemma is a result in system analysis and control theory which states: Given a number \gamma > 0, two n-vectors B, C and an n x n Hurwitz matrix A, if the pair (A,B) is completely controllable, then a symmetric matri ...

Hyperstability

In the early 1960s, Popov also conceived the notion of hyperstability, a concept that he viewed as generalization of absolute stability. This introduced a new and a very fruitful point of view for the analysis and synthesis of nonlinear feedback systems. This research work was published in the first half of the sixties and led to the book ''Hyperstability of Dynamic Systems'', first published in Romania in 1966, and subsequently translated into French and English (

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

, 1973). Popov was also the first to discover the geometric invariants of linear systems with respect to certain "transformation groups" and he introduced a "canonical" form for uniquely describing the multivariable systems.

References

*. {{DEFAULTSORT:Popov, Vasile M. 1928 births 20th-century American mathematicians Control theorists Living people People from Galați Romanian mathematicians Corresponding members of the Romanian Academy Romanian emigrants to the United States Politehnica University of Bucharest alumni Academic staff of the Politehnica University of Bucharest