Results 1  10
of
30
Transfer functions of regular linear systems Part III: Inversions And Duality
 Trans. Amer. Math. Soc
, 2000
"... We study four transformations which lead from one wellposed linear system to another: timeinversion, flowinversion, timeflowinversion and duality. Timeinversion means reversing the direction of time, flowinversion means interchanging inputs with outputs, while timeflowinversion means doing ..."
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Cited by 118 (18 self)
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We study four transformations which lead from one wellposed linear system to another: timeinversion, flowinversion, timeflowinversion and duality. Timeinversion means reversing the direction of time, flowinversion means interchanging inputs with outputs, while timeflowinversion means doing both of the inversions mentioned before. A wellposed linear system is timeinvertible if and only if its operator semigroup extends to a group. The system is flowinvertible if and only if its inputoutput map has a bounded inverse on some (hence, on every) finite time interval [0; ] ( > 0). This is true if and only if the transfer function of has a uniformly bounded inverse on some right halfplane. The system is timeflowinvertible if and only if on some (hence, on every) finite time interval [0; ], the combined operator from the initial state and the input function to the final state and the output function is invertible. This is the case, for example, if the system is conservative, since then is unitary. Timeowinversion can sometimes, but not always, be reduced to a combination of time and flowinversion. We derive a surprising necessary and sucient condition for to be timeflowinvertible: its system operator must have a uniformly bounded inverse on some left halfplane.
Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems. ESAIM: Control, Optimisation and Calculus of Variations, 7, 421–442. Ababacar Diagne received a Graduate Degree in Applied Mathematics and Computer Science
, 2002
"... Abstract. In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial dierential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperboli ..."
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Cited by 27 (1 self)
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Abstract. In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial dierential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of wellposed innitedimensional linear systems, we prove that the system is regular and derive various properties of its transfer functions, which are potentially useful for controller design. Our results remain valid for a wide class of processes governed by symmetric hyperbolic systems. Mathematics Subject Classication. 93D09, 93D25, 80A20, 35L50.
Integral Control of Linear Systems With Actuator Nonlinearities: Lower Bounds for the Maximal Regulating Gain
, 1999
"... Closing the loop around an exponentially stable singleinput singleoutput regular linear system, subject to a globally Lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller, is known to ensure asymptotic tracking of constant reference signals, provided that (a ..."
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Cited by 23 (18 self)
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Closing the loop around an exponentially stable singleinput singleoutput regular linear system, subject to a globally Lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller, is known to ensure asymptotic tracking of constant reference signals, provided that (a) the steadystate gain of the linear part of the plant is positive, (b) the positive integrator gain is sufficiently small and (c) the reference value is feasible in a very natural sense. Here we derive lower bounds for the maximal regulating gain for various special cases including systems with nonovershooting stepresponse and secondorder systems with a timedelay in the input or output. The lower bounds are given in terms of openloop frequency/step response data and the Lipschitz constant of the nonlinearity, and are hence readily obtainable.
Integral control of infinitedimensional systems in the presence of hysteresis: an inputoutput approach
 ESAIM: CONTROL, OPTIMISATION AND CALCULUS OF VARIATIONS
, 2007
"... This paper is concerned with integral control of systems with hysteresis. Using an inputoutput approach, it is shown that application of integral control to the series interconnection of either (a) a hysteretic input nonlinearity, an L2stable, timeinvariant linear system and a nondecreasing gl ..."
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Cited by 15 (11 self)
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This paper is concerned with integral control of systems with hysteresis. Using an inputoutput approach, it is shown that application of integral control to the series interconnection of either (a) a hysteretic input nonlinearity, an L2stable, timeinvariant linear system and a nondecreasing globally Lipschitz static output nonlinearity, or (b) an L2stable, timeinvariant linear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference signals, provided the positive integrator gain is smaller than a certain constant determined by a positivity condition in the frequency domain. The inputoutput results are applied in a general statespace setting wherein the linear component of the interconnection is a wellposed infinitedimensional system.
LowGain Integral Control of InfiniteDimensional Regular Linear Systems Subject to Input Hysteresis
, 1999
"... : We introduce a general class of causal dynamic nonlinearities with certain monotonicity and Lipschitz continuity properties. It is shown that closing the loop around an exponentially stable, singleinput, singleoutput, innitedimensional, regular, linear system, subject to an input nonlinearity f ..."
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Cited by 11 (9 self)
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: We introduce a general class of causal dynamic nonlinearities with certain monotonicity and Lipschitz continuity properties. It is shown that closing the loop around an exponentially stable, singleinput, singleoutput, innitedimensional, regular, linear system, subject to an input nonlinearity from this class and compensated by an integral controller, guarantees asymptotic tracking of constant reference signals, provided that (a) the steadystate gain of the linear part of the plant is positive, (b) the positive integrator gain is smaller than a certain constant given by a positivereal condition in terms of the linear part of the plant, and (c) the reference value is feasible in a very natural sense. The class of nonlinearities under consideration contains in particular relay hysteresis, backlash and hysteresis operators of Prandtl and Preisach type. Keywords: Regular innitedimensional systems; integral control; hysteresis nonlinearities; robust tracking. AMS subject classic...
Internal model based tracking and disturbance rejection for stable wellposed systems
 Automatica
, 2003
"... Abstract: In this paper we solve the tracking and disturbance rejection problem for infinitedimensional linear systems, with reference and disturbance signals that are superpositions of sinusoids. In one approach we use a low gain controller suggested by the internal model principle. In this appro ..."
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Cited by 11 (2 self)
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Abstract: In this paper we solve the tracking and disturbance rejection problem for infinitedimensional linear systems, with reference and disturbance signals that are superpositions of sinusoids. In one approach we use a low gain controller suggested by the internal model principle. In this approach, our results are a partial extension of results by T. Hämäläinen and S. Pohjolainen. In their papers, the plant is required to have an exponentially stable transfer function in the CallierDesoer algebra, while in this paper we only require the transfer function of the plant to be exponentially stable and wellposed. The conditions for a transfer function to be wellposed are sufficiently unrestrictive to be verifiable for many partial differential equations in more than one space variable. Our second approach concerns the case when the second component of the plant transfer function (from control input to tracking error) is positive. In this case, we identify a very simple stabilizing controller which is again an internal model, but which does not require low gain. We apply our results to two problems involving systems modeled by partial differential equations: the problem of rejecting external noise in a model for structure/acoustics interactions, and a similar problem for two coupled beams.
LowGain Integral Control of ContinuousTime Linear Systems Subject to Input and Output Nonlinearities
, 1999
"... : Continuoustime lowgain integral control strategies are presented for tracking of constant reference signals for nitedimensional, continuoustime, asymptotically stable, singleinput singleoutput, linear systems subject to a globally Lipschitz and nondecreasing input nonlinearity and a locally ..."
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Cited by 8 (7 self)
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: Continuoustime lowgain integral control strategies are presented for tracking of constant reference signals for nitedimensional, continuoustime, asymptotically stable, singleinput singleoutput, linear systems subject to a globally Lipschitz and nondecreasing input nonlinearity and a locally Lipschitz, nondecreasing and anely sectorbounded output nonlinearity (the conditions on the output nonlinearities may be relaxed if the input nonlinearity is bounded). Both nonadaptive (but possibly timevarying) and adaptive integrator gains are considered. In particular, it is shown that applying error feedback using an integral controller ensures asymptotic tracking of constant reference signals, provided that (a) the steadystate gain of the linear part of the plant is positive, (b) the positive integrator gain is ultimately suciently small and (c) the reference value is feasible in a very natural sense. The classes of actuator and sensor nonlinearities under consideration contain s...
TimeVarying And Adaptive Integral Control Of InfiniteDimensional Regular Linear Systems With Input Nonlinearities
 SIAM J. Control
, 1998
"... . Closing the loop around an exponentially stable, singleinput, singleoutput, regular, linear system  subject to a globally Lipschitz, nondecreasing actuator nonlinearity and compensated by an integral controller with timedependent gain k(t)  is shown to ensure asymptotic tracking of a const ..."
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Cited by 7 (7 self)
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. Closing the loop around an exponentially stable, singleinput, singleoutput, regular, linear system  subject to a globally Lipschitz, nondecreasing actuator nonlinearity and compensated by an integral controller with timedependent gain k(t)  is shown to ensure asymptotic tracking of a constant reference signal r, provided that (a) the steadystate gain of the linear part of the system is positive, (b) the reference value r is feasible in an entirely natural sense, and (c) the function t 7! k(t) monotonically decreases to zero at a sufficiently slow rate. This result forms the basis of a simple adaptive control strategy that ensures asymptotic tracking under conditions (a) and (b). Key words. adaptive control; infinitedimensional regular systems; input nonlinearities; integral control; saturation; robust tracking. AMS subject classifications. 34D05, 93C25, 93D05, 93D09, 93D15, 93D21 1. Introduction. The paper has, as precursor, the article [9] which contains an extension, to ...
TimeVarying and Adaptive DiscreteTime LowGain Control of InfiniteDimensional Linear Systems with Input Nonlinearities
 University of Bath
, 1998
"... : Discretetime lowgain control strategies are presented for tracking of constant reference signals for innitedimensional, discretetime, powerstable, linear systems subject to input nonlinearities. Both nonadaptive (but timevarying) and adaptive controls are considered. The discretetime resul ..."
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Cited by 6 (6 self)
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: Discretetime lowgain control strategies are presented for tracking of constant reference signals for innitedimensional, discretetime, powerstable, linear systems subject to input nonlinearities. Both nonadaptive (but timevarying) and adaptive controls are considered. The discretetime results are applied in the development of sampleddata integral control for innitedimensional, continuoustime, exponentially stable, regular, linear systems with input nonlinearities. Keywords: Discretetime systems; innitedimensional systems; integral control; input nonlinearities; regular systems; robust tracking; sampleddata control. AMS subject classications: 93C10, 93C20, 93C25, 93C55, 93C57, 93D09, 93D10, 93D21. 1 Introduction The paper extends a sequence [6, 7, 8] of recent results pertaining to integral control of innitedimensional systems subject to input nonlinearities. Underpinning these results are generalizations of the wellknown principle (see, for example, [4], [12] an...
Lack of timedelay robustness for stabilization of a structural acoustics model
 SIAM J. Control Optim
, 1999
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