PhD in Automatic Control, 10 years in Applied Research, next in Academia as University Professor of Systems and Control with research in Applied Mathematics.
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.
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.
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.
... 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 ...
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].
Publisher Summary This chapter analyzes approximations of delays by ordinary differential equatio... more Publisher Summary This chapter analyzes approximations of delays by ordinary differential equations. The approximation of functional differential equations by ordinary differential equations (ODE) occurred in the analog computation of the dynamical systems described by other types of equations than ODE. The simplest class of such systems is the class of linear time lag systems, and the transfer functions of such systems contain the transcendental function e−hσ. In analog computation, use was made of a certain approximation in the complex domain of an exponential by rational functions. The chapter obtains approximation results for new classes of time lag systems, particularly for those occurring from mixed initial boundary value problems for hyperbolic partial differential equations (PDE). It also points out the connection between these approximation results and the method of lines for hyperbolic PDE.
Consider a system $$y' = g\left( {t,y} \right)$$ (2.1.1) with g : R+ × R n → R n continuous. ... more Consider a system $$y' = g\left( {t,y} \right)$$ (2.1.1) with g : R+ × R n → R n continuous. Let ŷ be a solution defined on [t0, ∞).
Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application
This volume is dedicated to the 70th anniversary of Vasile Dr˘agan, an internationally recognized... more This volume is dedicated to the 70th anniversary of Vasile Dr˘agan, an internationally recognized researcher in the area of system and control theory. The impressive scientific results of Vasile Dragan are the output of a life-time 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
Abstract Starting from some pioneering papers in distributed parameter control systems for steam ... more Abstract Starting from some pioneering papers in distributed parameter control systems for steam turbines and their auxiliaries, a bilinear model for steam turbines with steam extraction and “long” steam pipes was elaborated and the feedback control synthesis has been performed using a suitable control Liapunov functional of quadratic type, both for distributed parameters systems and their lumped parameter approximation. The synthesized control ensures global stabilization of the steady state solution. It has been observed much later that the linearized steam wave propagation equations underlying the model were in fact a simplified linearized version of the conservation laws of the isentropic flow. Following this remark and bearing in mind the recent advances in the control of the systems described by conservation laws, the model of the combined heat electricity generation is re-written as a system which is linear in control; consequently the feedback stabilization also requires re-examination.
The paper presents some aspects of the evolution of the problem and tools for the absolute stabil... more The paper presents some aspects of the evolution of the problem and tools for the absolute stability problem, together with the extensions to other problems (forced and self sustained oscillations, instability, adaptive control).
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.
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.
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.
... 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 ...
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].
Publisher Summary This chapter analyzes approximations of delays by ordinary differential equatio... more Publisher Summary This chapter analyzes approximations of delays by ordinary differential equations. The approximation of functional differential equations by ordinary differential equations (ODE) occurred in the analog computation of the dynamical systems described by other types of equations than ODE. The simplest class of such systems is the class of linear time lag systems, and the transfer functions of such systems contain the transcendental function e−hσ. In analog computation, use was made of a certain approximation in the complex domain of an exponential by rational functions. The chapter obtains approximation results for new classes of time lag systems, particularly for those occurring from mixed initial boundary value problems for hyperbolic partial differential equations (PDE). It also points out the connection between these approximation results and the method of lines for hyperbolic PDE.
Consider a system $$y' = g\left( {t,y} \right)$$ (2.1.1) with g : R+ × R n → R n continuous. ... more Consider a system $$y' = g\left( {t,y} \right)$$ (2.1.1) with g : R+ × R n → R n continuous. Let ŷ be a solution defined on [t0, ∞).
Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application
This volume is dedicated to the 70th anniversary of Vasile Dr˘agan, an internationally recognized... more This volume is dedicated to the 70th anniversary of Vasile Dr˘agan, an internationally recognized researcher in the area of system and control theory. The impressive scientific results of Vasile Dragan are the output of a life-time 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
Abstract Starting from some pioneering papers in distributed parameter control systems for steam ... more Abstract Starting from some pioneering papers in distributed parameter control systems for steam turbines and their auxiliaries, a bilinear model for steam turbines with steam extraction and “long” steam pipes was elaborated and the feedback control synthesis has been performed using a suitable control Liapunov functional of quadratic type, both for distributed parameters systems and their lumped parameter approximation. The synthesized control ensures global stabilization of the steady state solution. It has been observed much later that the linearized steam wave propagation equations underlying the model were in fact a simplified linearized version of the conservation laws of the isentropic flow. Following this remark and bearing in mind the recent advances in the control of the systems described by conservation laws, the model of the combined heat electricity generation is re-written as a system which is linear in control; consequently the feedback stabilization also requires re-examination.
The paper presents some aspects of the evolution of the problem and tools for the absolute stabil... more The paper presents some aspects of the evolution of the problem and tools for the absolute stability problem, together with the extensions to other problems (forced and self sustained oscillations, instability, adaptive control).
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Papers by Vladimir B RASVAN