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In this paper, we develop a new approach to study gain operators built from the interconnection gains of infinite networks of dynamical systems. Our focus is on the construction of paths of strict decay which are used for building Lyapunov functions for the network and thus proving various stability properties, including input-to-state stability. Our approach is based on the study of an augmented gain operator whose fixed points are precisely the points of decay for the original gain operator. We show that plenty of such fixed points exist under a uniform version of the no-joint-increase condition. Using these fixed points to construct a path of strict decay, in general, requires specific dynamical properties of associated monotone operators. For particular types of gain operators such as max-type operators and subadditive operators, these properties follow from uniform global asymptotic stability of the system induced by the original gain operator. This is consistent with former results in the literature which can readily be recovered from our results. [ABSTRACT FROM AUTHOR]

In the original article [B. Jacob et al., SIAM J. Control Optim., 58 (2020), pp. 2952-2978] an unfortunate mistake appears in the definition of "norm-to-integral ISS." As the paper was the first to define the concept, we feel it necessary to point this out explicitly. [ABSTRACT FROM AUTHOR]

This paper develops a large-scale small-gain result for dynamic networks composed of infinite-dimensional subsystems. It is assumed that the subsystems are input-to-output stable (IOS) and unboundedness observable (UO), and the large-scale infinite-dimensional system can be proved to be IOS and UO if the proposed small-gain condition is satisfied. [ABSTRACT FROM AUTHOR]

In this paper, we treat the problem of practical feedback stabilization for a class of nonlinear infinite-dimensional control systems by means of an observer. A compensator design is given under a restriction of the perturbed term that the perturbations is bounded by the sum of a Holder continuous function and a Lipschitz function where the nominal system is supposed to be exponentially stabilizable by a linear feedback. The results are illustrated with an example. [ABSTRACT FROM AUTHOR]

This paper addresses the following question: "Suppose that a state-feedback controller stabilizes an infinite-dimensional linear continuous-time system. If we choose the parameters of an event/self-triggering mechanism appropriately, is the event/self-triggered control system stable under all sufficiently small nonlinear Lipschitz perturbations?" We assume that the stabilizing feedback operator is compact. This assumption is used to guarantee the strict positiveness of inter-event times and the existence of the mild solution of evolution equations with unbounded control operators. First, for the case where the control operator is bounded, we show that the answer to the above question is positive, giving a sufficient condition for exponential stability, which can be employed for the design of event/self-triggering mechanisms. Next, we investigate the case where the control operator is unbounded and prove that the answer is still positive for periodic event-triggering mechanisms. [ABSTRACT FROM AUTHOR]

In this paper, first, we prove the projective measurement increases the entropy in infinite-dimensional quantum systems, and discuss some useful properties for the study of entropy changes in quantum measurement. Next, we introduce a joint purification framework which keeps track of all the information transfer in a quantum measurement. Based on this joint purification which encodes the various entropies arising from the most general quantum measurement, we establish several information conservation and entropic relations in infinite-dimensional case. [ABSTRACT FROM AUTHOR]

In the present paper, preliminary results towards the generalization to the infinite-dimensional setting of some well-known robust finite-dimensional control algorithms are illustrated. More specifically, we deal with the tracking problem for some classes of linear uncertain infinite-dimensional systems evolving in Hilbert spaces. We design distributed variable-structure stabilizers that are shown to be effective in the presence of external disturbances. The main focus of the present paper is on the rejection of nonvanishing external disturbances. The generalization to the infinite-dimensional setting of the well-known finite-dimensional controllers, namely the "power-fractional" controller [S. P. Bhat and D. S. Bernstein, SIAM J. Control Optim., 38 (2000), pp. 751-766] and two second-order sliding-mode" control algorithms (the "twisting" and "supertwisting" algorithms [L. Fridman and A. Levant, Higher order sliding modes as a natural phenomenon in control theory, in Robust Control via Variable Structure and Lyapunov Techniques, Springer-Verlag, Berlin, 1996, pp. 107-133; A. Levant, Internat. J. Control, 58 (1993). pp. 1247-1263]), is the main contribution of the present investigation. First, the "distributed twisting" control algorithm is developed In address the asymptotic state tracking of the perturbed wave equation. Next, the finite-time state tracking of the unperturbed heat equation is provided by means of a "distributed power-fractional" controller. Finally, the "distributed supertwisting" controller is suggested to address the asymptotic state tracking of the heat equation in spite of the presence of persistent disturbances. Constructive proofs of stability are developed via the Lyapunov functional technique, which leads to simple tuning rules for the controller parameters. Simulation results are discussed to verify the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

Suppose that a continuous-time linear infinite-dimensional system with a static state-feedback controller is strongly stable. We address the following question: If we convert the continuous-time controller to a sampled-data controller by applying an idealized sampler and a zeroorder hold, will the resulting sampled-data system be strongly stable for all sufficiently small sampling periods? In this paper, we restrict our attention to the situation where the generator of the open-loop system is a Riesz-spectral operator and its point spectrum has a limit point at the origin. We present conditions under which the answer to the above question is affirmative. In the robustness analysis, we show that the sufficient condition for strong stability obtained in the Arendt--Batty--Lyubich--V\~u theorem is preserved between the original continuous-time system and the sampled-data system under fast sampling. [ABSTRACT FROM AUTHOR]

Problems involving control of large ensembles of structurally identical dynamical systems, called ensemble control, arise in numerous scientific areas from quantum control and robotics to brain medicine. In many of such applications, control can only be implemented at the population level, i.e., through broadcasting an input signal to all the systems in the population, and this new control paradigm challenges the classical systems theory. In recent years, considerable efforts have been made to investigate controllability properties of ensemble systems, and most works emphasized on linear and some forms of bilinear and nonlinear ensemble systems. In this paper, we study controllability of a broad class of bilinear ensemble systems defined on semisimple Lie groups, for which we define the notion of ensemble controllability through a Riemannian structure of the state space Lie group. Leveraging the Cartan decomposition of semisimple Lie algebras in representation theory, we develop a covering method that decomposes the state space Lie group into a collection of Lie subgroups generating the Lie group, which enables the determination of ensemble controllability by controllability of the subsystems evolving on these Lie subgroups. Using the covering method, we show the equivalence between ensemble and classical controllability, i.e., controllability of each individual system in the ensemble implies ensemble controllability, for bilinear ensemble systems evolving on semisimple Lie groups. This equivalence makes the examination of controllability for infinite-dimensional ensemble systems as tractable as for a finite-dimensional single system. [ABSTRACT FROM AUTHOR]

This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combined with a linear-quadratic state feedback controller for a system of hyperbolic PDEs. The design is based on the duality fact between the control design and the observer design. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to a fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the temperature and the reactant concentration in a fixed-bed reactor is investigated by using the developed algorithm, which lead to express the jacket temperature (manipulated variable) as a feedback of the estimated temperature and concentration in the reactor. [ABSTRACT FROM AUTHOR]

In Cao and Wang (J. Phys.: Math. Theor. 40, 3507-3542, 2007), the revised geometric measure of entanglement (RGME) for states in finite dimensional bipartite quantum systems was proposed. Furthermore, in Cao and Wang (Commun. Theor. Phys. 51(4), 613-620, 2009), the authors obtained the revised geometry measure of entanglement for multipartite states including three-qubit GHZ state, W state, and the generalized Smolin state in the presence of noise and the two-mode squeezed thermal state, and defined the Gaussian geometric entanglement measure. In this paper, we generalize the RGME to infinite dimensional multipartite quantum systems, and prove that this measure satisfies some necessary properties as a well-defined entanglement measure, including monotonicity under local operations and classical communications. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary order N ∈ ℕ on a bounded 1-dimensional spatial domain (a, b). In order to achieve stabilization, we couple the system to a dynamic boundary controller, that is, a controller that acts on the system only via the boundary points a, b of the spatial domain. We use a nonlinear controller in order to capture the nonlinear behavior that realistic actuators often exhibit and, moreover, we allow the output of the controller to be corrupted by actuator disturbances before it is fed back into the system. What we show here is that the resulting nonlinear closed-loop system is input-to-state stable w.r.t. square-integrable disturbance inputs. In particular, we obtain uniform input-to-state stability for systems of order N = 1 and a special class of nonlinear controllers, and weak input-to-state stability for systems of arbitrary order N ∈ ℕ and a more general class of nonlinear controllers. Also, in both cases, we obtain convergence to 0 of all solutions as t →∞. Applications are given to vibrating strings and beams. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the gradient stabilisation of infinite-dimensional bilinear systems. Then under sufficient conditions, we establish exponential, strong and weak gradient stabilisation. The obtained results are illustrated by simulations. [ABSTRACT FROM AUTHOR]

This paper considers a general class of infinite-dimensional linear control systems described by either a state-space (SCS) or boundary control (BCS) system formulation. A key objective of the paper is to accomplish trajectory planning of a BCS through a 'stable' dynamic inversion without resorting to discretization. To this end, the paper first formulates the particular solution of an infinite-dimensional SCS within a Sobolev space together with a set of necessary and sufficient conditions for its existence and an explicit formula for computing it. The resulting solution, which may be noncausal, is further utilized to explicitly compute the bounded control input needed for output tracking of a BCS without requiring its inverse to be minimum phase or even to possess a $$C_{0}$$ -semigroup. The key results of the paper are illustrated on a flexible beam and a one-dimensional heat conduction system. [ABSTRACT FROM AUTHOR]

This paper deals with the observer design problem for time-varying linear infinite-dimensional systems. We address both the problem of online estimation of the state of the system from the output via an asymptotic observer, and the problem of offline estimation of the initial state via a back and forth nudging algorithm. In both contexts, we show under a weak detectability assumption that a Luenberger-like observer may reconstruct the so-called observable subspace of the system. However, since no exact observability hypothesis is required, only a weak convergence of the observer holds in general. Additional conditions on the system are required to show the strong convergence. We provide an application of our results to a batch crystallization process modeled by a one-dimensional transport equation with periodic boundary conditions, in which we try to estimate the crystal size distribution from the chord length distribution. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we derive some inequalities about the relative entropy for infinite-dimensional quantum systems. Secondly, we propose a new measurement based on the relative entropy of entanglement for infinite-dimensional systems with bounded mean energy, and give a lower bound on this entanglement measure. Lastly, we generalize this measure to multi-partite quantum systems. [ABSTRACT FROM AUTHOR]

In a pedagogical but exhaustive manner, this survey reviews the main results on input-tostate stability (ISS) for infinite-dimensional systems. This property allows for the estimation of the impact of inputs and initial conditions on both the intermediate values and the asymptotic bound on the solutions. ISS has unified the input-output and Lyapunov stability theories and is a crucial property in the stability theory of control systems as well as for many applications whose dynamics depend on parameters, unknown perturbations, or other inputs. In this paper, starting from classic results for nonlinear ordinary differential equations, we motivate the study of the ISS property for distributed parameter systems. Then fundamental properties are given, such an ISS superposition theorem and characterizations of (global and local) ISS in terms of Lyapunov functions. We explain in detail the functional-analytic approach to ISS theory of linear systems with unbounded input operators, with special attention devoted to ISS theory of boundary control systems. The Lyapunov method is shown to be very useful for both linear and nonlinear models, including parabolic and hyperbolic partial differential equations. Next, we show the efficiency of the ISS framework in studying the stability of large-scale networks, coupled either via the boundary or via the interior of the spatial domain. ISS methodology allows for the reduction of the stability analysis of complex networks, by considering the stability properties of its components and the interconnection structure between the subsystems. An extra section is devoted to ISS theory of time-delay systems with the emphasis on techniques that are particularly suited for this class of systems. Finally, numerous applications are considered for which ISS properties play a crucial role in their study. The survey contains recent as well as classical results on systems theory and suggests many open problems. [ABSTRACT FROM AUTHOR]

The active disturbance rejection control (AD RC), first proposed by Jingqing Han in late 1980s, is a powerful control technology being able to deal with external disturbances and internal uncertainties in large scale for control systems in engineering applications. This survey paper will articulate, from a theoretical perspective, the origin, ideology and progress of ADRC for not only uncertain finite-dimensional systems but also uncertain infinite-dimensional ones. Some recent theoretical developments, general framework and unsolved problems of ADRC for finite-dimensional systems with mismatched disturbances and uncertainties by output feedback, uncertain finite-dimensional stochastic systems, uncertain infinite-dimensional systems described by both the wave equation and the fractional-order partial differential equation are successively addressed, from which we see the challenges and opportunities for this remarkable emerging control technology to various types of control systems. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of event-triggered control for infinite-dimensional systems. We employ event-triggering mechanisms that compare the plant state and the error of the control input induced by the event-triggered implementation. Under the assumption that feedback operators are compact, a strictly positive lower bound on the interevent times can be guaranteed. We show that if the threshold of the event-triggering mechanisms is sufficiently small, then the event-triggered control system with a bounded control operator and a compact feedback operator is exponentially stable. For infinite-dimensional systems with unbounded control operators, we employ two event-triggering mechanisms that are based on system decomposition and periodic eventtriggering, respectively, and then analyze the exponential stability of the closed-loop system under each event-triggering mechanism. [ABSTRACT FROM AUTHOR]

In the paper, the initial observability of abstract second-order infinite-dimensional dynamical systems is considered. Two cases of observation operator are explored. First, the observation operator is assumed to be bounded. Then results are extended to more general class of observations related to the observation operators that are assumed to be bounded with respect to square root of elasticity operator which covers the case of some unboundedness in observation. Using the frequency-domain method it is proved, that initial observability of second-order system under discussion can be verified by the initial observability conditions for the corresponding simplified first-order system. General results are then applied for initial observability investigation of infinite dimensional systems described by partial differential equations modelling flexible mechanical structures. Some special cases are also discussed and practical comments and remarks are given. The paper extends earlier results on initial observability for a class of infinite-dimensional second-order abstract dynamical systems. [ABSTRACT FROM AUTHOR]

We establish well-posedness results for non-autonomous semilinear input-output systems, the central assumption being the scattering-passivity of the considered semilinear system. Along the way, we also establish global stability estimates. We consider both systems with distributed control and observation and systems with boundary control and observation, and we treat them in a unified manner. Applications are given to nonlinearly controlled collocated systems and to nonlinearly controlled port-Hamiltonian systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider mixed H/ H control problems for linear infinite-dimensional systems. The first part considers the state feedback control for the H/ H control problems of linear infinite-dimensional systems. The cost horizon can be infinite or finite time. The solutions of the H/ H control problem for linear infinitedimensional systems are presented in terms of the solutions of the coupled operator Riccati equations and coupled differential operator Riccati equations. The second part addresses the observer-based H/ H control of linear infinite-dimensional systems with infinite horizon and finite horizon costs. The solutions for the observer-based H/ H control problem of linear infinite-dimensional systems are represented in terms of the solutions of coupled operator Riccati equations. The first-order partial differential system examples are presented for illustration. In particular, for these examples, the Riccati equations are represented in terms of the coefficients of first-order partial differential systems. [ABSTRACT FROM AUTHOR]

This paper is devoted to two issues. The first one is to provide Lyapunov-based tools to establish integral input-to-state stability (iISS) and input-to-state stability (ISS) for some classes of nonlinear parabolic equations. The other one is to provide a stability criterion for interconnections of iISS parabolic systems. The results addressing the former problem allow us to overcome obstacles arising in tackling the latter one. The results for the latter problem are a small-gain condition and a formula of Lyapunov functions which can be constructed for interconnections whenever the small-gain condition holds. It is demonstrated that for interconnections of partial differential equations, the choice of a right state and input spaces is crucial, in particular for iISS subsystems which are not ISS. As illustrative examples, stability of two highly nonlinear reaction-diffusion systems is established by the proposed small-gain criterion. [ABSTRACT FROM AUTHOR]

We generalize the results in Yu and Liu (Phys. Rev. Lett. 95, 150504, 2005) and Hou and Guo (Int. J. Theor. Phys. 50, 1245–1254, 2011) to infinite-dimensional systems and answer a problem raised in the second paper. Consider a bipartite system H ⊗ K with dimH = dimK = ∞. We show that (1) for any orthonormal sequences { E k } k = 1 ∞ and { F k } k = 1 ∞ consist of observables respectively in C 2 (H) and C 2 (K) , if ∑ k E k ⊗ F k converges under the weak operator topology and if W = I - ∑ k E k ⊗ F k is not positive, then W is a decomposable entanglement witness; (2) every state ρ of system H ⊗ K has a Schmidt decomposition ρ = ∑ k δ k E k ⊗ F k with {Ek} and {Fk} orthonormal sequences of observables. [ABSTRACT FROM AUTHOR]

Flexible structures have been increasingly utilized in many applications because of their light-weight and low production cost. However, being flexible leads to vibration problems. Vibration suppression of flexible structures is a challenging control problem because the structures are actually infinite-dimensional systems. In this paper, an adaptive control scheme is proposed for the vibration suppression of a piezo-actuated flexible beam. The controller makes use of the configuration of the prominent proportional-integral-derivative controller and is derived using an infinite-dimensional Lyapunov method. In contrast to existing schemes, the present scheme does not require any approximated finite-dimensional model of the beam. Thus, the stability of the closed loop system is guaranteed for all vibration modes. Experimental results have illustrated the feasibility of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, we review the infinite-dimensional version of Uhlmann's theorem of quantum fidelity. Based on this important theorem, we derive some useful properties of quantum fidelity for infinite-dimensional quantum systems. Next, we study the fidelity in the infinite-dimensional discrete-time quantum filters associated Markov chain, and prove that it is a sub-martingale. [ABSTRACT FROM AUTHOR]

This paper is concerned with the eigenvalue decay of solution operators to operator Lyapunov equations, a relevant topic in the context of model reduction for parabolic control problems. We mainly focus on the Gramian operator, which arises in the context of control and observation of heat processes in infinite time, which is normally the first step towards observations in a finite time horizon. By improving existing energy and observability estimates for parabolic equations, we obtain both upper and lower bounds on the convergence rate of the eigenvalues of the Gramian operator towards zero. Both bounds follow the same polynomial decay rate, up to a multiplicative constant, which ensures their optimality. This confirms the slow decay of the eigenvalues and limits the efficiency of model reduction. The theoretical findings are supported by numerical results. [ABSTRACT FROM AUTHOR]

This paper deals with the stabilization of a non isothermal tubular reactor in which convection, diffusion and chemical reaction occur. The tubular reactor is modelled by a set of non-linear partial differential equations and the distributed jacket temperature is used as control input. Two stabilizing control laws are derived using the thermodynamic availability function as a Lyapunov function. It is shown how the closed loop performances, in terms of settling time and input control amplitude can be improved by modifying the availability function. Simulation results show the effectiveness of the proposed state feedback controls. • Non-linear control laws to the stabilization of tubular reactors are designed • Availability function is used as Lyapunov function from thermodynamic considerations. • Reduced availability function is proposed as Lyapunov function for stabilization. • Simulation results show the effectiveness of the proposed state feedback controls. [ABSTRACT FROM AUTHOR]

We consider the class of spatially decaying systems, where the underlying dynamics are spatially decaying and the sensing and controls are spatially distributed. This class of systems arises in various applications where there is a notion of spatial distance with respect to which couplings between the subsystems can be quantified using a class of coupling weights. We exploit the spatial decay property of the underlying dynamics of this class of systems by introducing a class of sparsity and spatial localization measures. We develop a new methodology based on concepts of q-Banach algebras of spatially decaying matrices that enables us to establish a relationship between spatial decay properties of spatially decaying systems and their sparsity and spatial localization features. Moreover, it is shown that the inverse-closedness property of matrix algebras plays a central role in exploiting various structural properties of spatially decaying systems. We characterize conditions for exponential stability of spatially decaying system over q-Banach algebras and prove that the unique solutions of the Lyapunov and Riccati equations over a proper q-Banach algebra also belong to the same q-Banach algebra. It is shown that the quadratically optimal state feedback controllers for spatially decaying systems are sparse and spatially localized in the sense that they have near-optimal sparse information structures. [ABSTRACT FROM AUTHOR]

This paper derives exact formulas for singular values and vectors of Hankel operators whose symbol is a product of a single-input single-output inner function and a multi-input multi-output rational function. This class of Hankel operators arises from the sensitivity minimization H∞ control problem with a rational weight function and the approximation problem of transfer functions having rational outer parts. It is shown that there is a Hamiltonian transcendental equation characterizing singular values which leads to a matrix function formula for singular vectors. [ABSTRACT FROM AUTHOR]

This work is dedicated to the stability analysis of time-delay systems with a single constant delay using the Lyapunov–Krasovskii theorem. This approach has been widely used in the literature and numerous sufficient conditions of stability have been proposed and expressed as linear matrix inequalities (LMI). The main criticism of the method that is often pointed out is that these LMI conditions are only sufficient, and there is a lack of information regarding the reduction of the conservatism. Recently, scalable methods have been investigated using Bessel–Legendre inequality or orthogonal polynomial-based inequalities. The interest of these methods relies on their hierarchical structure with a guarantee of reduction of the level of conservatism. However, the convergence is still an open question that will be answered for the first time in this paper. The objective is to prove that the stability of a time-delay system implies the feasibility of these scalable LMI, at a sufficiently large order of the Legendre polynomials. Moreover, the proposed contribution is even able to provide an analytic estimation of this order, giving rise to a necessary and sufficient LMI for the stability of time-delay systems. [ABSTRACT FROM AUTHOR]

In this paper we present results about the algebraic Riccati equation (ARE) and a weaker version of the ARE, the algebraic Riccati system (ARS), for infinite-dimensional, discrete-time systems. We introduce an operator pencil, associated with these equations, the so-called extended symplectic pencil (ESP). We present a general form for all linear bounded solutions of the ARS in terms of the deflating subspaces of the ESP. This relation is analogous to the results of the Hamiltonian approach for the continuous-time ARE and to the symplectic pencil approach for the finite-dimensional discrete-time ARE. In particular, we show that there is a one-to-one relation between deflating subspaces with a special structure and the solutions of the ARS. Using the relation between the solutions of the ARS and the deflating subspaces of the ESP, we give characterizations of self-adjoint, nonnegative, and stabilizing solutions. In addition we give criteria for the discrete-time, infinite-dimensional ARE to have a maximal self-adjoint solution. Furthermore, we consider under which conditions a solution of the ARS satisfies the ARE as well. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of systems described by singular integrodifferential equations. This type of systems appear, for example, in the modeling of certain aeroelastic control problems. We study these systems in frequency domain framework and show the existence of finite-dimensional stabilizing controllers. An algorithmic procedure is outlined for the construction of such controllers. In order to illustrate the numerical aspects of this algorithm, we present an example involving the classical Theodorsen model of an airfoil, which fits in the class of systems considered here. [ABSTRACT FROM AUTHOR]

Relative entropies play important roles in classical and quantum information theory. In this paper, we discuss the sandwiched Rényi relative entropy for α∈(0,1) on 풯(H)+ (the cone of positive trace-class operators acting on an infinite-dimensional complex Hilbert space H) and characterize all surjective maps preserving the sandwiched Rényi relative entropy on 풯(H)+. Such transformations have the form T↦cUTU∗ for each T∈풯(H)+, where c>0 and U is either a unitary or an anti-unitary operator on H. Particularly, all surjective maps preserving sandwiched Rényi relative entropy on 풮(H) (the set of all quantum states on H) are necessarily implemented by either a unitary or an anti-unitary operator. [ABSTRACT FROM AUTHOR]

Boundary feedback control design for systems of linear hyperbolic conservation laws in the presence of boundary measurements affected by disturbances is studied. The design of the controller is performed to achieve input-to-state stability (ISS) with respect to measurement disturbances with a minimal gain. The closed-loop system is analyzed as an abstract dynamical system with inputs. Sufficient conditions in the form of dissipation functional inequalities are given to establish an ISS bound for the closed-loop system. The control design problem is turned into an optimization problem over matrix inequality constraints. Semidefinite programming techniques are adopted to devise systematic control design algorithms reducing the effect of measurement disturbances. The effectiveness of the approach is extensively shown in several numerical examples. [ABSTRACT FROM AUTHOR]

This paper deals with frequency domain robust regulation of signals generated by an infinite-dimensional exosystem. The problem is formulated and the stability types are chosen so that one can generalize the existing finite-dimensional theory to more general classes of infinitedimensional systems and signals. The main results of this article are extensions of the internal model principle, of a necessary and sufficient solvability condition for the robust regulation problem, and of Davison's simple servo compensator for stable plants in the chosen algebraic framework. [ABSTRACT FROM AUTHOR]

Flexible beams are parts of lighter structures and flexible manipulators, which possess numerous advantages. However, the flexibility leads to a vibration problem. This paper presents an experimental study of active vibration control of flexible beams. The beam assumed to behave according to the Euler-Bernoulli theory is modeled by a partial differential equation. The control objective is to suppress the vibration of the beam. Based on the Lyapunov stability theory of infinite-dimension systems, a control law is directly derived without using any approximated finite-dimensional model of the beam. The success of the controller is experimentally demonstrated on a cantilever aluminum beam with a laser displacement sensor and a piezoelectric actuator. Experimental results show that the controller effectively suppresses the vibration. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we discuss the state feedback output regulation problem (SFRP) for infinite-dimensional linear control systems with infinite-dimensional exosystems. Under the polynomial stabilizability assumption, sufficient and necessary conditions are given for the solvability of the SFRP. The solvability of this problem is characterized in terms of the solvability of a pair of linear regulator equations. An application of the solvability of the SFRP for polynomial stable SISO system is given. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, an internal-model-based controller (IMBC) is designed to reject an external signal generated by a class of infinite-dimensional systems for a class of nonlinear systems. First, a new description of the external signal is proposed. By this new description, the IMBC is designed, and the resulting closed-loop error dynamics are analyzed with the help of a Lyapunov-Krasovskii functional. Compared with existing IMBCs, the designed IMBC provides the flexibility to cope with more types of external signals as well as to choose controller parameters to achieve a tradeoff between rejection performance and stability. Finally, the method is applied to attitude control of a quadrotor aircraft. Effectiveness of the IMBC is demonstrated by simulation. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In this paper block circulant and block Toeplitz long strings of MIMO systems with finite length are compared with their corresponding infinite-dimensional spatially invariant systems. The focus is on the convergence of the sequence of solutions to the control Riccati equations and the convergence of the sequence of growth bounds of the closed-loop generators. We show that block circulant approximants of infinite-dimensional spatially invariant systems reflect well the LQR behavior of the infinite-dimensional systems. An example of an exponentially stabilizable and exponentially detectable infinite-dimensional system is also considered in this paper. This example shows that the growth bounds of the Toeplitz approximants, as the length of the string increases, and the growth bound of the corresponding infinite-dimensional model, can be significantly different. On the positive side, we give sufficient conditions for the convergence of the growth bounds. [Copyright &y& Elsevier]

Flow controllers are needed to avoid congestion in different types of networks. The dynamics of such networks, however, can usually be represented by infinite-dimensional models, which are either based on partial-differential equations or delay-differential equations. An optimal ℋ∞ flow controller design approach has recently been proposed for networks whose dynamics involve multiple and uncertain time-varying time delays. In the present paper, performance level and stability margins of controllers designed by this approach are analyzed. It is shown that, by choosing certain controller design parameters large, stability margins can be improved; while choosing them small improves performance levels. Therefore, there is a clear trade-off between robustness and performance. [ABSTRACT FROM PUBLISHER]