Papers by Vladimir B RASVAN
Springer proceedings in mathematics & statistics, 2024
Linear canonical (Hamiltonian) systems are familiar to the engineering community both from Ration... more Linear canonical (Hamiltonian) systems are familiar to the engineering community both from Rational Mechanics and Control. In Rational Mechanics an “evergreen” problem is that of the λ-zones of stability in connection with parametric resonance while in Control these systems belong to the field of Linear Quadratic Theory, being strongly connected to Matrix Riccati Equation. In both cases some robustness problems are met but they deal with different classes of systems: totally stable in the first and hyperbolic in the second case. The present survey gives an account of these topics especially of their discrete-time counterpart.
HAL (Le Centre pour la Communication Scientifique Directe), Aug 1, 2005
Opuscula Mathematica, 2022
This paper starts from several applications described by initial/boundary value problems for 1D (... more This paper starts from several applications described by initial/boundary value problems for 1D (time and one space variable) hyperbolic partial differential equations whose basic properties and stability of equilibria are studied throughout the same properties for certain associated neutral functional differential equations. It is a common fact that asymptotic stability for neutral functional differential equations is normally obtained under the assumption of asymptotic stability of the difference operator associated to the aforementioned neutral functional differential equations. However the physically meaningful applications presented in the paper have the associated difference operator(s) in critical cases (their stability is, generally speaking, non-asymptotic). Consequently the stability of the considered application models is either non-asymptotic or fragile (in a sense introduced in the paper). The models represent an overview gathered from various fields, processed here in order to emphasize the associated neutral functional differential equations which, consequently, are a challenge to the usual approaches. In the concluding part there are suggested possible ways to overcome these difficulties.
IFAC Proceedings Volumes, 2013
Abstract As shown by its title, the aim of this paper is twofold. Firstly, the equation of Nichol... more Abstract As shown by its title, the aim of this paper is twofold. Firstly, the equation of Nicholson describing population dynamics is interesting in itself since it is a straightforward example of time delay equation where the delay appears naturally in the models as a consequence of the (here biological) phenomenon. On the other hand the nonlinearity occurring in this equation is a sector restricted one and incorporating the stability problems in an absolute stability one makes sense. The main result of the paper is the positive answer to the associated delay independent Aizerman conjecture.
HAL (Le Centre pour la Communication Scientifique Directe), 2003
International audienc
International Journal of Robust and Nonlinear Control, Jun 28, 2021
Throughout the paper there are considered engineering applications leading to neutral functional ... more Throughout the paper there are considered engineering applications leading to neutral functional differential equations having marginally stable difference operator. This aspect makes asymptotic stability questionable or at least fragile with respect to delay uncertainties. In the case of synchronizing mechanical oscillators, the marginally stable (in critical case) difference operator can be a possible explanation for the so‐called complex behavior. Some hints for improving the stability of the difference operator are given.
Lecture Notes in Control and Information Sciences, 2012
Since the very first paper of J. Bernoulli in 1728, a connection exists between initial boundary ... more Since the very first paper of J. Bernoulli in 1728, a connection exists between initial boundary value problems for hyperbolic Partial Differential Equations (PDE) in the plane (with a single space coordinate accounting for wave propagation) and some associated Functional Equations (FE). The functional equations may be difference equations (in continuous time), delay-differential (mostly of neutral type) or even integral/integro-differential. It is possible to discuss dynamics and control either for PDE or FE since both may be viewed as self contained mathematical objects. A more recent topic is control of systems displaying conservation laws. Conservation laws are described by nonlinear hyperbolic PDE belonging to the class “lossless” (conservative). It is not without interest to discuss association of some FE. Lossless implies usually distortionless propagation hence one would expect here also lumped time delays. The paper contains some illustrating applications from various fields: nuclear reactors with circulating fuel, canal flows control, overhead crane, without forgetting the standard classical example of the nonhomogeneous transmission lines for distortionless and lossless propagation. Specific features of the control models are discussed in connection with the control approach wherever it applies.
IFAC Proceedings Volumes, Dec 1, 1996
The classical one-mass model for road vehicle dynamics in lateral motion is considered as basic f... more The classical one-mass model for road vehicle dynamics in lateral motion is considered as basic for such actual problems as: 4-wheel steering or fully automatic steering of cars. Starting from the robustness problem a decoupling scheme based on controned servo has been proposed. This paper provides a stability analysis of this algorithm based on frequency methods for the classical problem of absolute stability. This approach is motivat.ed by the Wlcertainty introduced by the tire-road characteristics: it leads to consider a class of nonlinear functions satisfying sector-type and slope restrictions. This stability analysis is directed finally to estimate a rather important merit figure of a road vehicle -the critical speed-lntroduced from stability considerations for the lateral motion.
IFAC Proceedings Volumes, 2006
Starting from various models in control and electrical engineering, there is obtained a rather ge... more Starting from various models in control and electrical engineering, there is obtained a rather general model of an IBVP(Initial Boundary Value Problem) for hyperbolic PDE(Partial Differential Equations) with the boundary conditions connected in feedback to some systems described by ODE(Ordinary Differential Equations -lumped parameter systems). To this model it is associated a special class of FDE(Functional Differential Equations) -delay equations coupled to continuous time difference equations. This survey examines stability and oscillation problems for such systems within the framework underlined by the dialectics Liapunov function/Popov frequency domain inequalities. Several open problems are equally mentioned.
Advances in Difference Equations, 2006
The main purpose of the paper is to give discrete-time counterpart for some strong (robust) stabi... more The main purpose of the paper is to give discrete-time counterpart for some strong (robust) stability results concerning periodic linear Hamiltonian systems. In the continuoustime version, these results go back to Liapunov and Žukovskii; their deep generalizations are due to Kreȋn, Gel'fand, and Jakubovič and obtaining the discrete version is not an easy task since not all results migrate mutatis-mutandis from continuous time to discrete time, that is, from ordinary differential to difference equations. Throughout the paper, the theory of the stability zones is performed for scalar (2nd-order) canonical systems. Using the characteristic function, the study of the stability zones is made in connection with the characteristic numbers of the periodic and skew-periodic boundary value problems for the canonical system. The multiplier motion ("traffic") on the unit circle of the complex plane is analyzed and, in the same context, the Liapunov estimate for the central zone is given in the discrete-time case.
Proc. fourth Int. Conf. on Dynamical Systems and Differential Equations, Wilmington NC, May 24-27, 2002), Discrete and Continuous Dynamical Systems , Apr 1, 2003
In this paper we start from the discrete version of linear Hamiltonian systems with periodic coef... more In this paper we start from the discrete version of linear Hamiltonian systems with periodic coefficients $_y_(k+1) - _y(_k) = \\lambda B(__k)_y(_k) + \\lambda D_(k^z_(k+1))$ $_z_(k+1) - _z(_k) = -\\lambda A(__k)_y(_k) - \\lambda B*_(k^z_(k+1))$ where $A_k$ and $D_k$ are Hermitian matrices, $A_k$, $B_k$, $D_k$ define $N$-periodic sequences, and $\\lambda$ is a complex parameter. For this system a Krein-type theory of the $\\lambda$-zones of strong (robust) stability may be constructed. Within this theory the side $\\lambda$-zones’ width may be estimated using the multipliers’ “traffic rules” of Krein while the central stability zone (centered around $\\lambda$ = 0) is estimated using the eigenvalues of a certain boundary value problem which is self-adjoint. In the discrete-time there occur some specific differences with respect to the continuous time case due to the fact that the transition matrix (hence the monodromy matrix also) is not entire with respect to $\\lambda$ but rational. During the paper we consider some specific cases (the matrix analogue of the discretized Hill equation, the J-unitary and symplectic systems, real scalar systems) for which the results on the eigenvalues are complete and obtain some simplified estimates of the central stability zones.
Ima Journal of Mathematical Control and Information, Mar 1, 1997
The simple idea of Hinrichsen & Pritchard (1986a,b), who defined the structured stability rad... more The simple idea of Hinrichsen & Pritchard (1986a,b), who defined the structured stability radius, has proved to be unexpectedly fruitful, generating a large amount of work and making interesting connections (Hinrichsen & Pritchard 1988, 1989; Hinrichsen & Motscha 1988; Hinrichsen et al. 1989; Hinrichsen & Son 1991; Pritchard & Townley 1989, 1990; Rasvan 1993). In this paper we shall discuss stability radii for a class of applications concerning systems with propagation. Such systems are described by simple lossless telegraph equations and include the practical cases of physical systems containing lossless steam, gas, or water pipes or electrical circuits containing lossless LC transmission lines. We shall state in a natural way the problem of a structured stability radius for such models. To estimate such radii we shall use a frequency-domain approach of Popov (1973) and Yakubovich (1978), as suggested by the known formulae of Hinrichsen & Pritchard. Our specific models lead to a general differential difference equation coupled with a diference equation.lt could be possible to express such systems as abstract evolution equations (see for instance the paper of Weiss (1994) on regular systems) and then use the general results by Pritchard & Townley (1990). We do not intend here to compete with such approach. Our aim here is to point out some examples of naturally occuring, practical problems where the stability radius has to be considered and then to draw attention to the possibility of approaching the problem with •methods similar to the ones used in absolute stability. It is hoped that existence of several approaches to the problem will stimulate further research concerning comparisons between them, both from the view-point of the tightness of estimates as well as from the view-point of simplicity, directness, and accessibility.
This volume is dedicated to the 70th anniversary of Vasile Drȃgan, an internationally recognized ... more This volume is dedicated to the 70th anniversary of Vasile Drȃgan, an internationally recognized researcher in the area of system and control theory. The impressive scientific results of Vasile Dragan are the output of a lifetime sustained work and his special talent for Mathematics. This is a story of "A Beautiful Mind". On this occasion, his collaborators and his colleagues wish him long life in good health and happiness, and more achievements in the field of science.
International Journal of Systems Science, Oct 1, 1991
Feedback systems with several differentiable non-linearities are considered. For the absolute sta... more Feedback systems with several differentiable non-linearities are considered. For the absolute stability problem a frequency domain criterion is obtained incorporating only slope information about non-linearities and containing a multiplier of the form P + (iω)Q, where P and Q are diagonal matrices. For the case of a single non-linearity, connections with similar results of other authors are discussed.
Springer eBooks, 1993
As it has been shown in the introductory part, the stability studies for chemical processes are c... more As it has been shown in the introductory part, the stability studies for chemical processes are connected with prolonged operation of chemical plants around the steady state. Chemical systems are subject to disturbances like: variations of initial concentrations of the reactor input substances, modifications of environment thermodynamic parameters, substance flow variations, control system signals.
This paper focuses on forced oscillations (periodic and almost periodic) in some dynamical models... more This paper focuses on forced oscillations (periodic and almost periodic) in some dynamical models described by coupled differential and difference equations. The existence and stability result is based on a theorem on invariant manifolds Banach spaces due to Kurzweil and Halanay. The state-space (based on Liapunov-Krasovskii functionals combined with the 5-procedure) approach is considered. An illustrative example is presented and some conclusions are drawn concerning sharpness and easiness in applications of the method.
The paper aims to apply linear quadratic theory of periodic sytems (due to Yakubovich) to the cas... more The paper aims to apply linear quadratic theory of periodic sytems (due to Yakubovich) to the case of existence. uniqueness and stability of forced nonlinear oscillations bringing together periodic Hamiltonians and periodic Riccati equations with nonlinear systems with periodic coefficients having a periodic or almost periodic forcing term. This allows obtaining sufficient conditions for the existence of forced nonlinear periodic or almost periodic oscillations expressed in terms of an associated periodic linear Hamiltonian. These conditions might be checked numerically via the established methods for periodic systems.
Birkhäuser Basel eBooks, 2000
... solution is stabilizable in the following sense: if the controlled system (21) Xk+ l= Akxk+ b... more ... solution is stabilizable in the following sense: if the controlled system (21) Xk+ l= Akxk+ bknk is considered, by choosing the control (input) sequence as follows (22) fik=-(=-b* kHk+ ibkJ (-ck-A* kHk+ ibkj xk the" closed loop" linear system -l (23)**+ i= Ak-bkl=-bkHk+ ibk) I-ck-A ...
Systems & Control Letters, Feb 1, 1990
Abstract Motivated by a problem in factorization of periodic nodes, a new condition for existence... more Abstract Motivated by a problem in factorization of periodic nodes, a new condition for existence of a stabilizing periodic solution to a matrix differential Riccati equation is proved in connection to a theorem of Yakubovich [4].
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Papers by Vladimir B RASVAN