A generalized orthonormal basis for linear dynamical systems

In this paper, the probability of controllability of a class of linear dynamical systems is investigated by applying simple combinatorial reasoning (in the manner of Porter 1972) to the structure of the mode-controllability matrices of systems of this class. The results of this investigation are discussed in relation to the results concerning the probability of stability of linear dynamical systems obtained by Ashby (1952) and Porter (1972).

This paper is concerned with tele‐presence and tele‐operation of autonomous vehicles over the Additive White Gaussian Noise (AWGN) channel. This wireless communication channel is subject to transmission noise and transmission power constraint. An encoder, decoder and controller are proposed by implementing a novel linearization method for linearizing the nonlinear dynamic systems at operating points. For the linearized systems, the encoder, decoder and controller are implemented that were previously proposed for output tracking as well as stability of linear dynamic systems. Two novel linearization methods are proposed and their satisfactory performances are proved for output tracking as well as stability of nonlinear dynamic system. The first method is based on the fixed linearization rate and the second one is based on the variable (optimal) linearization rate. The decoder that is based on the second method is in fact the extended Kalman filter with the optimal linearization rate. The performances of these two methods are compared with each other and the other proposed methods by implementing them to the problems of the tele‐presence and tele‐operation of autonomous vehicles over the AWGN channel. Their satisfactory performances are illustrated. It is illustrated that the second method has higher computational complexity with slightly better performance and is applicable to a larger class of reference trajectories.

In this paper, we introduced and explored the Laguerre and Kautz functions as an orthonormal functions based of model predictive control approach for automotive applications with particularly focuses on vehicle path following control and motor position control. The first implementation starting with the known trajectory, model predictive control based on linearized vehicle and tire model was used to follow the desired trajectory as close as possible, we performed a vehicle at middle speed maneuver on double lane change scenario. In the second application; predictive control is designed in order to track the desired motor position. We compared the predictive controllers designed based on Delta, Laguerre and Kautz functions for both applications in term of tracking error and position error performances. The result showed that the predictive control based on Kautz function gave a better tracking performance compared to Laguerre function and Delta function (conventional method). However, Laguerre function is easier and simpler in term of algorithm implementation than the other two functions. Moreover, for all functions based on predictive control; the simulation results demonstrated that orthonormal function can be implemented in predictive control approaches particularly to automotive application, thus, it is believe can be extended to other applications.

Given a stable linear time-invariant dynamical system x·= Ax, it is shown that there exists a related stable family of dynamical systems x·=A(k)x. The Lyapunov stability criterion remains valid for all linear operators A(k)=DkA of this family.

In many engineering applications, continuous-time models are preferred to discrete-time ones, in that they provide good physical insight and can be derived also from non-uniformly sampled data. However, for such models, model selection is a hard task if no prior physical knowledge is given. In this paper, we propose a non-parametric approach to infer a continuous-time linear model from data, by automatically selecting a proper structure of the transfer function and guaranteeing to preserve the system stability properties. By means of benchmark simulation examples, the proposed approach is shown to outperform state-of-the-art continuous-time methods, also in the critical case when short sequences of canonical input signals, like impulses or steps, are used for model learning.

This paper presents a sufficient condition that establishes closed loop stability for linear time invariant dynamical systems with transfer functions that are analytic in the open right half complex plane. The condition is suitable for analyzing a large class of highly complex, possibly interconnected, systems. The result is based on bounding Nyquist curves by using frequency dependent half planes. It provides (usually non-trivial) robustness guarantees for the provably stable systems and generalizes to the multidimensional case using matrix field of values. Concrete examples illustrate the applications of the condition. From our condition, it is easy to derive a relaxed version of the classical result that the interconnection of a positive real and strictly positive real linear system under feedback is closed loop stable.

Finite time identification in unstable linear systems

The authors establish a generalized frequency-domain criterion for checking families of polynomials for root confinement in open subsets of the complex plane. The authors show how this criterion reduces to checking certain curves in the complex plane for zero confinement. Moreover, in some special cases, it further reduces to some complex functions with pointwise phase differences that are always less than pi in magnitude. Most of the currently available results on the robust stability of linear systems with parametric uncertainties can be viewed within the unifying frequency-domain framework presented. The framework encapsulates not just finite-dimensional systems, but any linear-time-invariant (LTI) system that can be characterized by transfer functions of a single variable. It also covers robust stability of LTI systems under passive feedback. >

The Popov criterion for the stability of linear, time-invariant, finite-dimensional systems with a single non-linearity has been generalized by a numbers of authors through a relaxation of the single non-linearity and the finite-dimensional constraints in order to be applicable to a wider range of practical problems. This paper extends these results further by relaxing the time-invariant constraint. It is shown that a covariance condition when satisfied is a sufficient condition for the system output to be bounded and square integrable for zero input conditions.

We consider linear dynamical systems including random variables to model uncertainties of physical parameters. The output of the system is expanded into a series with orthogonal basis functions. Our aim is to identify a sparse approximation, where just a low number of basis functions is required for a sufficiently accurate representation. The coefficient functions of the expansion are approximated by a quadrature method or a sampling technique. The performance of a quadrature scheme can be described by a larger linear dynamical system, which is weakly coupled. We apply methods of model order reduction to the coupled system, which results in a sparse approximation of the original expansion. The approximation error is estimated by Hardy norms of transfer functions. Furthermore, we present numerical results for a test example modelling the electric circuit of a band pass filter.

The methodology of estimation and control theory is considered in terms of response, stability, estimation, and control of linear dynamic systems. Within the context of discrete-time systems, multi-input, multi-output, nth-order linear systems are discussed, and general results for optimal estimation, optimal control, and other topics are presented. The application of these results to modeling human behavior is considered with special emphasis on man-machine system models.

Introduction: This article is the result of the research “Analysis of the dynamic systems component of the engineering programs in control and automation and technology in industrial electronics,” developed at the Francisco José de Caldas District University in the years 2022-2023. Problem: The document addresses the lack of a clear and comprehensive structure in the analysis of linear dynamic systems, as well as the absence of an innovative approach to addressing these topics in traditional courses, which hinders their understanding and application in different disciplines. Objective: The objective is to present a novel approach to analyzing linear dynamic systems, providing a complete framework of concepts, relationships, and important tools in this analysis, as well as a literature review based on over seventeen years of experience in courses and studies of this kind. Methodology: A journey of concepts is proposed from signals and systems, through modeling with methods such as black box, white box, gray box, to linear analysis based on examples with calculation of differential equations, state representation, transfer function, and block diagrams. Results: The document aggregates and articulates all the concepts of dynamic systems, along with the relationships and tools used, offering a more practical and intuitive approach to understanding the material. Conclusion: The document provides a comprehensive and articulated view of key concepts in the analysis of linear dynamic systems, highlighting an innovative approach that facilitates their understanding. Its main contribution is to aggregate and articulate these concepts, along with the tools and relationships used, to offer a more practical and clear approach for their study. Originality: The originality lies in proposing a novel and structured approach to analyzing linear dynamic systems, addressing the lack of clarity and completeness in traditional approaches. Limitations: Although the document proposes a novel approach, it does not delve into specific aspects of some topics covered, which could limit the detailed understanding of certain concepts. Deepening: The document could delve into the practical application of the proposed concepts and tools in real cases of dynamic systems, as well as into the comparison with traditional approaches to highlight the differences and advantages of the proposed new approach.

It is shown that two properties of rational transfer functions with real coefficients are realized by means of a single complex IIR digital filter. Equivalently, the real and imaginary parts of output from a complex filter for a real input sequence correspond to real coefficient transfer function respectively. In a real signal processing, a delay operator z/sup -1/ corresponds to a real operation. In this case, a complex transfer function is formed by connecting two real transfer functions with an imaginary unit. These real functions are approximated to the desired properties and are expressed by a complex coefficient transfer function.

Choice of Units, Column Sums, and Stability in Linear Dynamic Systems with Nonnegative Square Matrices

Choice of Units, Column Sums, and Stability in Linear Dynamic Systems with Nonnegative Square Matrices