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Popov Criterion
In nonlinear control and stability theory, the Popov criterion is a stability criterion discovered by Vasile M. Popov for the absolute stability of a class of nonlinear systems whose nonlinearity must satisfy an open-sector condition. While the circle criterion can be applied to nonlinear time-varying systems, the Popov criterion is applicable only to autonomous (that is, time invariant) systems. System description The sub-class of Lur'e systems studied by Popov is described by: : \begin \dot & = Ax+bu \\ \dot & = u \\ y & = cx+d\xi \end \begin u = -\varphi (y) \end where ''x'' ∈ R''n'', ''ξ'',''u'',''y'' are scalars, and ''A'',''b'',''c'' and ''d'' have commensurate dimensions. The nonlinear element Φ: R → R is a time-invariant nonlinearity belonging to ''open sector'' (0, ∞), that is, Φ(0) = 0 and ''y''Φ(''y'') > 0 for all ''y'' not equal to 0. Note that the system studied by Popov has a pole at the origin and there is no direct pass-through from input to out ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stability Criterion
In control theory, and especially stability theory, a stability criterion establishes when a system is stable. A number of stability criteria are in common use: *Circle criterion *Jury stability criterion *Liénard–Chipart criterion *Nyquist stability criterion *Routh–Hurwitz stability criterion *Vakhitov–Kolokolov stability criterion *Barkhausen stability criterion Stability may also be determined by means of root locus analysis. Although the concept of stability is general, there are several narrower definitions through which it may be assessed: * BIBO stability * Linear stability * Lyapunov stability * Orbital stability In mathematical physics and the theory of partial differential equations, the solitary wave solution of the form u(x,t)=e^\phi(x) is said to be orbitally stable if any solution with the initial data sufficiently close to \phi(x) forever remains ... {{sia Stability theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vasile M
The male name Vasile is of Greek origin and means "King". Vasile is a male Romanian given name or a surname. It is equivalent to the English name Basil. As a given name As a surname *Cristian Vasile (1908–1985), Romanian tango-romance singer *Nicolae Vasile (born 1995), Romanian professional footballer *Niculina Vasile (born 1958), former Romanian high jumper * Radu Vasile (1942–2013), Romanian politician and Prime Minister *Ștefan Vasile (born 1982), Romanian Olympic canoer Places *Pârâul lui Vasile, a river in Romania * Valea lui Vasile, a river in Romania * Vasile Aron (Sibiu district) See also * Vasiliu (surname) * Vasilescu (surname) * Vasilievca (other) * Vasile Alecsandri (other) * Vasileuți Vasileuți is a commune in Rîșcani District, Moldova Moldova ( , ; ), officially the Republic of Moldova ( ro, Republica Moldova), is a Landlocked country, landlocked country in Eastern Europe. It is bordered by Romania to the west ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Criterion
In nonlinear control and stability theory, the circle criterion is a stability criterion for nonlinear time-varying systems. It can be viewed as a generalization of the Nyquist stability criterion for linear time-invariant (LTI) systems. Overview Consider a linear system subject to non-linear feedback, i.e. a non linear element \varphi(v, t) is present in the feedback loop. Assume that the element satisfies a sector condition mu_1,\mu_2/math>, and (to keep things simple) that the open loop system is stable. Then the closed loop system is globally asymptotically stable if the Nyquist locus does not penetrate the circle having as diameter the segment 1/\mu_1,-1/\mu_2/math> located on the ''x''-axis. General description Consider the nonlinear system In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Invariant
In control theory, a time-invariant (TIV) system has a time-dependent system function that is not a direct function of time. Such systems are regarded as a class of systems in the field of system analysis. The time-dependent system function is a function of the time-dependent input function. If this function depends ''only'' indirectly on the time-domain (via the input function, for example), then that is a system that would be considered time-invariant. Conversely, any direct dependence on the time-domain of the system function could be considered as a "time-varying system". Mathematically speaking, "time-invariance" of a system is the following property: :''Given a system with a time-dependent output function , and a time-dependent input function , the system will be considered time-invariant if a time-delay on the input directly equates to a time-delay of the output function. For example, if time is "elapsed time", then "time-invariance" implies that the relationship be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vasile M Popov
Vasile Mihai Popov (born 1928) is a leading systems theorist and control engineering specialist. He is well known for having developed a method to analyze stability of nonlinear dynamical systems, 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 Polytechnic Institute 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. In 1968 Popov left Romania. He was a visiting professor at the Electrical Engineering departments of University of California, Berkeley, and Stanford University, and then Professor in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Routh Hurwitz Stability Criterion
Routh may refer to: Places * Routh, East Riding of Yorkshire, a village in England People * Brandon Routh (born 1979), American actor * Camilla Belle Routh (born 1986), American actress * Edward Routh (1831–1907), British mathematician * Francis John Routh (1927–2021), English composer and author * Jonathan Routh (1927–2008), British humourist * Josh Routh (born 1978), contemporary American circus artist * Martin Joseph Routh Martin Joseph Routh (18 September 175522 December 1854) was an English classical scholar and President of Magdalen College, Oxford (1791–1854). Birthplace and Oxford career Routh was born at South Elmham, Suffolk, son of the Rev. Peter Rou ..., or Martin Routh (1755-1854), British classical scholar * C.R.N. Routh, wrote '' Who's Who in Tudor England 1485-1603'' {{disambig, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Globally Asymptotically Stable
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 second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions. For certain classes of ODEs, the existence of Lyapunov functions is a necessary and sufficient condition for stability. Whereas there is no general technique for constructing Lyapunov functions for ODEs, in many specific cases the construction of Lyapunov functions is known. For instance, quadratic functions suffice for systems with one state; the solution of a particular linear matrix inequality provides Lyapunov functions for linear systems; and conservation laws can often be used to construct Lyapunov fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Criterion
In nonlinear control and stability theory, the circle criterion is a stability criterion for nonlinear time-varying systems. It can be viewed as a generalization of the Nyquist stability criterion for linear time-invariant (LTI) systems. Overview Consider a linear system subject to non-linear feedback, i.e. a non linear element \varphi(v, t) is present in the feedback loop. Assume that the element satisfies a sector condition mu_1,\mu_2/math>, and (to keep things simple) that the open loop system is stable. Then the closed loop system is globally asymptotically stable if the Nyquist locus does not penetrate the circle having as diameter the segment 1/\mu_1,-1/\mu_2/math> located on the ''x''-axis. General description Consider the nonlinear system In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Control
Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback, feedforward, or signal filtering. The system to be controlled is called the " plant". One way to make the output of a system follow a desired reference signal is to compare the output of the plant to the desired output, and provide feedback to the plant to modify the output to bring it closer to the desired output. Control theory is divided into two branches. Linear control theory applies to systems made of devices which obey the superposition principle. They are governed by linear differential equations. A major subclass is systems which in addition have parameters which do not change with time, called '' linear time invariant'' (L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
