Stability of Discrete Linear Feedback Systems with Pulse-Width-Modulation Power Dispatch

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

The article is dedicated to optimizing the digital current control loop of a thyristor converter-driven electric drive, essential for ensuring stable, precise, and reliable operation of electric drives in automated and industrial systems. The primary goal of this research is to develop and enhance the digital current regulator (DCR), which enables the drive system to achieve desired performance, including rapid and stable response to current changes without excessive overshoot or oscillations. Optimization of the current loop improves energy efficiency, enhances dynamic properties, and increases resistance to external disturbances, all of which are critical for modern electric drive systems. The introduction discusses key aspects of digital current loop optimization, specifically dynamic characteristics such as time delays, sampling rate, and bandwidth, which significantly impact the efficiency of digital controllers. Special attention is given to the tuning of proportional-integral (PI) controller parameters, allowing quick and stable response to current changes. The developed model allows preliminary simulation of the current loop’s performance, providing an opportunity to test different configurations before actual implementation. To improve the accuracy and stability of the system, filtering methods are proposed to reduce the impact of high-frequency noise, ensuring the system’s precision and robustness against external interference. Optimization criteria are introduced, including minimizing the integral square error (ISE) and reducing energy consumption, which significantly decreases system losses and increases the energy efficiency of electric drives. In developing the optimized control loop, the following assumptions are considered: 1) the thyristor converter (TC) operates in continuous current mode, 2) the current loop dynamics are studied within a narrow range of TC phase angle changes, and 3) a discrete dynamic TC model is used with averaging of electromotive force (EMF) over the conduction interval. Optimizing the digital current loop addresses several critical tasks, including enhancing control accuracy, reducing overshoot and oscillations, and improving the system’s dynamic response, allowing for reduced delays and a faster reaction to load changes. The optimization results of the digital current regulator (DCR) show reduced energy consumption and significant improvements in control accuracy. The high-speed performance of the digital current loop enables fast transient processes within a single sampling interval of the thyristor converter, which is crucial for systems requiring rapid regulation. Additionally, the digital control loop provides flexibility in control, as it allows for system adjustments to different operating conditions through a software-based approach. The study’s final results demonstrate the potential of digital current loops in modern electric drives. With advances in microprocessor technology, digital regulators enable more complex control algorithms, including adaptive and predictive strategies, which further enhance system efficiency. These approaches are especially relevant for industrial electric drives that require high precision and response speed, making digital current loops a promising solution for contemporary automated control systems.

Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems

In the paper sufficient conditions for stability of nonlinear discrete systems with iterations and for synthesis of discrete Lagrange stable linear time-varying system with iterations, connecting the norm of the operator describing the discrete system, the initial conditions, the perturbations and the parameters of the systems are given and proven with theorems. The results can be used for assessment of discrete iterative processes and systems, like digital microprocessor based controllers.

: This report considers a feedback control law for linear time-varying and time invariant discrete systems based on a receding horizon concept applied to a minimum energy problem with fixed terminal constraints. The control law is shown to be asymptotically stable and to result in a new method for stabilizing linear time-varying systems as well as extending some well known methods for stabilizing time invariant systems. In particular, the stabilizing gains of the feedback control law are obtained from the solution to a discrete Riccati equation over an arbitrary finite time interval, which is relatively easy to compute. The gain matrix reduces to a constant matrix for linear time invariant systems. Some stability results will turn out to be special cases of these results. The results parallel those for linear continuous time systems, although the technical details are tedious and more involved.

The geometric properties of the canonical parameter space are used to derive necessary conditions for constraining zeros to lie within or on a central circular region of radius α in the z-plane. These necessary conditions are then compared with the sufficient conditions for the stability of linear discrete time systems.

This paper mainly discusses the robust quadratic stability and stabilization of linear discrete time stochastic systems with state delay and uncertain parameters. By means of the linear matrix inequality (LMI) method, a sufficient condition is respectively obtained for the stability and stabilizability of the considered system. Moreover, an example with simulations is given to verify the effectiveness of our theoretical results.

Some extensions on recent work in passive stability theory by Desoer and the author are presented. The stability of feedback systems is considered where the forward-loop and return-loop subsystems each have been subdivided into several systems operating in parallel. Results are obtained in the areas of Lyapunov stability, L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> input L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> output stability, and bounded-input bounded-state stability. Before applying these results to a specific multiloop feedback system, a pseudoenergy analysis must be done on each sub sub-system. Two specific types of systems are so analyzed. The first is a general linear first-order time-varying system. The second is a linear time-varying infinite-dimensional system; the analysis of this system takes the form of a Kalman-Yacubovich-type lemma. By using these two new systems, along with several others that have been analyzed previously, stability theorems for many specific multiloop feedback systems can be proven. One such example is given.

This paper extends some of the basic results in the area of Lyapunov (asymptotic) and finite time and practical stability to linear, discrete, time invariant time-delay systems. New definitions have been established for the latter concept of stability. Sufficient conditions for this type of stability, concerning the particular class of linear discrete time-delay systems are derived. To the best knowledge of the authors, such results have not yet been reported. Moreover, the generalization of some previous results, in the area of Lyapunov stability for the same class of systems has been also established and proven.

This note deals with the delay-dependent stability and stabilization of linear system with state and input delays. Firstly, for the nominal system, by introducing the augmented Lyapunov functional and some free-weighting matrices, new delay-dependent stability and stabilization criteria of the system are presented. Then, these new conditions are extended to handle norm-bounded uncertain systems with state and input delays, which show less conservativeness. Numerical examples are given to illustrate the effectiveness of the proposed results.

In this article, the problem of nonfragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli distribution. A new approach called the “state-transition matrix method” is introduced and some necessary and sufficient conditions are derived to solve the underlying stabilization problem. The Lyapunov theorem based on the state-transition matrix also makes a contribution to the discrete finite-time control theory. One practical example is provided to validate the effectiveness of the newly proposed control strategy.

This paper presents the stabilization problem of a class of discrete-time stochastic linear systems with time delay using an event-triggered control(ETC) strategy. For the general linear systems, we propose a new event triggering mechanism and deduce sufficient conditions for mean square exponentially stabilizability(MSES) and almost sure exponentially stabilizability(ASES) via ETC. The results show that the stability of the system depends on the system parameters (time delay, noise, event trigger threshold parameter, and unstable characteristic value of the original system). When the feedback control is disturbed by low-intensity noise, the unstable system can be stable in the mean square. Finally, the validity of the theoretical results is illustrated through a simulation example.

Robust linear controller design of uncertain discrete systems with time-varying delay

Stability of non-conservative linear discrete gyroscopic systems

Recently improved sufficient conditions for the L^{p} stability of multiple-input multiple-output linear time-invariant feedback systems are given. The continuous-time case is done in detail; the discrete-time case is outlined. Unstable open-loop systems with singular residue matrices are allowed.