Interplay between discretization and controllability of linear delay systems: An algebraic viewpoint

For linear delay systems with limited controls the notion of a proper control system is introduced. If the uncontrolled system \dot{x}(t)= Ax(t)+ Bx(t-h) is uniformly asymptotically stable and the control equation \dot{x}(t)=Ax(t)+Bx(t-)+Cu(t) is proper, then the control system is Euclidean null-controllable. We note that controllability is equivalent to the system being proper for delay systems with unlimited power.

Controllability of linear delay systems and of their sampled versions

Control of Linear Delay Systems

This article presents the central finite-dimensional H ∞ controller for linear time-varying systems with unknown parameters, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H ∞ controller problem to the corresponding H 2 controller problem, using the technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H 2 and H Infinity Control Problems’, IEEE Transactions Automatic Control, 34, 831–847]. This article yields the central suboptimal H ∞ controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H 2 controller obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008), ‘Optimal LQG Controller for Linear Systems with Unknown Parameters’, Journal of The Franklin Institute, 345, 293–302]. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H ∞ controller for linear systems with exactly known parameter values.

In this paper, we deal with discrete‐time linear control systems in which the state is constrained to lie in the positive orthant independently of the inputs involved, that is, the inputs can take negative values. Such (positive state) systems appear, for example, in ecology models where the removal of individuals from a population is described. Controllability and reachability are fundamental properties of a system that show its ability to move in space, which are analyzed from an algebraic point of view throughout the text, paying special attention to the single‐input case. Copyright © 2017 John Wiley & Sons, Ltd.

Network Control.- Delay-Based Non-linear Observers for Congestion Control in Communication Networks.- On the Use of State Predictors in Networked Control Systems.- Networked Control Systems: Algorithms and Experiments.- Modeling and Closed Loop Control for Resource-Constrained Load Balancing with Time Delays in Parallel Computations.- Stability of Load Balancing Control.- Teleoperation.- Robust H ? Control of Bilateral Teleoperation Systems Under Communication Time-Delay.- Web Remote Control of Mechanical Systems: Delay Problems and Experimental Measurements of Round Trip Time.- PDE Approach for Time Delays in Robotized Teleoperation.- Emerging Methodologies.- From Time Delay to Distributed Parameter Systems in Communications.- Computing Maximum Delay Deviation Allowed to Retain Stability in Systems with Two Delays.- On Exact Controllability of Linear Time Delay Systems of Neutral Type.- New Computational Methods.- Applied Interval Computation: A New Approach for Time-Delays Systems Analysis.- Mathematical and Computational Tools for the Stability Analysis of Time-Varying Delay Systems and Applications in Mechanical Engineering.- Diffusive Representation for Operators Involving Delays.- OreModules: A Symbolic Package for the Study of Multidimensional Linear Systems.- Predictors, Inversion and Filtering.- Inversion and Tracking Problems for Time Delay Linear Systems.- Finite Impulse Response Systems for Almost Perfect Decoupling in Nonminimum-Phase Plants.- Linearization of the Power Amplifier in Mobile Telecommunications.- Merging Saturations and Input Delays.- Robust Sampled-Data Control: An Input Delay Approach.- Stabilization and Finite-Gain Stabilizability of Delay Linear Systems Subject to Input Saturation.- Global Asymptotic Stabilization of a PVTOL Aircraft Model with Delay in the Input.

The controllability of linear time-invariant systems with a time delay in the control function is studied.

SummaryAt the present time, there is a great deal of interest in the adaptive control of systems with rapidly varying parameters. Such problems arise in different forms and in many disciplines including finance, sociology, biology, and engineering. In general, these problems are intractable mathematically and the time variations have to be classified in some form to obtain rigorous results. In this paper, we consider the adaptive identification and control of linear systems with periodically varying parameters (referred to as linear time‐varying periodic (LTP) systems). The class of systems with known periodic parameters has been investigated widely since the pioneering work of Floquet and lends itself to rigorous mathematical analysis. However, very little was known until the early years of the last decade concerning the adaptive control of such systems. The problem was introduced by Xu and explored in detail by Narendra and Zhiling in 2006 and 2009, respectively. In 2012, a new method was introduced in adaptive control by Han and Narendra and is referred to as second‐level adaptation. In this paper, the adaptive identification and control of LTP systems using second‐level adaptation is discussed.

This paper focuses on the synthesis problem of robust and reliable H/sup /spl infin// control for linear systems with norm-bounded time-varying parameter uncertainty in the state and delayed-state matrices, and also with actuator failures among a pre-specified subset of actuators. Actuator failures are considered as disturbance signals of arbitrary values to the system. A linear matrix inequality (LMI) method is given for the memoryless state feedback synthesis problem to quadratically stabilize the given systems with H/sup /spl infin//-norm bound constraints on attenuation of augmented disturbances, including failure signals in cases of actuator failures for any admissible uncertainty. The results depend on the size of the time-delay via the use of a Razumikhin-type theorem.

Performance limits and deconstraints of linear feedback control systems disturbed by random noise are studied from the viewpoint of information theory. By using Bode integral formulas, information transmission in such systems is connected to unstable poles and nonminimum phase zeros of open-loop transfer functions. Performance limits of disturbance rejection are discussed by using such connection, and the conservation law of variety is revised based on a new extended definition of variety. Meanwhile, a necessary information condition which implies a new kind of design constraints of linear tracking problem is proposed with the concept of mutual information rate, and the law of requisite variety is derived from this condition.

Let G be a connected Lie group with Lie algebra g. This review is devoted to studying the fundamental dynamic properties of elements in the normalizer NG of G. Through an algebraic characterization of NG, we analyze the different dynamics inside the normalizer. NG contains the well-known left-invariant vector fields and the linear and affine vector fields on G. In any case, we show the shape of the solutions of these ordinary differential equations on G. We give examples in low-dimensional Lie groups. It is worth saying that these dynamics generate the linear and bilinear control systems on Euclidean spaces and the invariant and linear control systems on Lie groups. Moreover, the Jouan Equivalence Theorem shows how to extend this theory to control systems on manifolds.

Robust control for a networked direct-drive linear motion control system: Design and experiments

In this work, we consider linear and nonlinear fractional stochastic delay systems driven by the Rosenblatt process. With the aid of the delayed Mittag-Leffler matrix functions and the representation of solutions of these systems, we derive the controllability results as an application. By introducing a fractional delayed Gramian matrix, we provide sufficient and necessary criteria for the controllability of linear fractional stochastic delay systems. Furthermore, by employing Krasnoselskii’s fixed point theorem, we establish sufficient conditions for the controllability of nonlinear fractional stochastic delay systems. Finally, an example is given to illustrate the main results.

In the field of control theory, there has been an increase in interest in studies on the equivalence of robust and optimum control of linear control systems. To provide appropriate constraints for increased stability and control performance, we study in this work the link between linear systems under robust and optimum control as well as the equivalence between the two. We will present in this research significant changes to the way constraints are designed, which may also improve system control and stability. We will show that with theorems and examples.

On the K-theory of feedback actions on linear systems