A Higher-Order Method for Dynamic Optimization of Controllable Linear Time-Invariant Systems

This work describes a new procedure for dynamic optimization of controllable linear time-invariant (LTI) systems. Unlike the traditional approach, which results in 2 n first-order differential equations, the method proposed here yields a set of m differential equations, whose highest order is twice the controllability index of the system p. This paper generalizes the approach presented in a previous work to any controllable LTI system.

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A Higher-Order Method for Dynamic Optimization of Controllable LTI Systems

ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1 ◽

10.1115/dscc2011-5964 ◽

2011 ◽

Author(s):

Damiano Zanotto ◽

Sunil K. Agrawal ◽

Giulio Rosati

Keyword(s):

Differential Equations ◽

Dynamic Optimization ◽

Linear Time ◽

Traditional Approach ◽

Linear Time Invariant ◽

System P ◽

Lti System ◽

Higher Order Method ◽

Time Invariant ◽

Controllability Index

This work describes a new procedure for dynamic optimization of controllable Linear time-invariant (LTI) systems. Unlike the traditional approach, which results in 2n first order differential equations, the method proposed here yields a set of m differential equations, whose highest order is twice the controllability index of the system p. This paper generalizes the approach presented in a previous work [1] to any controllable LTI system.

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Complete Controllability of Impulsive Fractional Linear Time-Invariant Systems with Delay

Abstract and Applied Analysis ◽

10.1155/2013/374938 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 5

Author(s):

Xian-Feng Zhou ◽

Song Liu ◽

Wei Jiang

Keyword(s):

Dynamical Systems ◽

Differential Equations ◽

Fractional Differential Equations ◽

Linear Time ◽

Complete Controllability ◽

Linear Time Invariant ◽

Impulsive Fractional Differential Equations ◽

Fractional Differential ◽

Linear Time Invariant Systems ◽

Time Invariant

Some flaws on impulsive fractional differential equations (systems) have been found. This paper is concerned with the complete controllability of impulsive fractional linear time-invariant dynamical systems with delay. The criteria on the controllability of the system, which is sufficient and necessary, are established by constructing suitable control inputs. Two examples are provided to illustrate the obtained results.

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Basics to Multirate Systems

Multirate Filtering for Digital Signal Processing ◽

10.4018/978-1-60566-178-0.ch002 ◽

2009 ◽

pp. 23-63

Author(s):

Ljiljana Milic

Keyword(s):

Linear Time ◽

Sampling Rate ◽

Multirate Systems ◽

Linear Time Invariant ◽

Lti System ◽

Linear Time Invariant Systems ◽

Time Invariant ◽

The Given

Linear time-invariant systems operate at a single sampling rate i.e. the sampling rate is the same at the input and at the output of the system, and at all the nodes inside the system. Thus, in an LTI system, the sampling rate doesn’t change in different stages of the system. Systems that use different sampling rates at different stages are called the multirate systems. The multirate techniques are used to convert the given sampling rate to the desired sampling rate, and to provide different sampling rates through the system without destroying the signal components of interest. In this chapter, we consider the sampling rate alterations when changing the sampling rate by an integer factor. We describe the basic sampling rate alteration operations, and the effects of those operations on the spectrum of the signal.

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Identification of Linear Time Invariant Systems Using FMCW Signals and Stretch Processing Receivers

International Journal of Advances in Telecommunications Electrotechnics Signals and Systems ◽

10.11601/ijates.v8i2.276 ◽

2019 ◽

Vol 8 (2) ◽

pp. 35

Author(s):

Stephan Häfner ◽

Reiner Thomä

Keyword(s):

Continuous Wave ◽

Linear Time ◽

Practical Applications ◽

Fmcw Radar ◽

Linear Time Invariant ◽

Time Bandwidth Product ◽

Lti System ◽

Baseband Signal ◽

Linear Time Invariant Systems ◽

Time Invariant

The paper deals with the identification of linear time invariant (LTI) systems by a special observer. An observer emitting an frequency modulated continuous wave (FMCW) signal and having a stretch processor as receiver will be considered for system identification. A thorough derivation of the gathered baseband signal for arbitrary LTI systems will be given. It is shown, that the received signal is approximately given by the transfer function of the LTI system over the frequency sweep of the FMCW signal. The proof relies on an infinite large time-bandwidth product of the transmit signal, such that errors remain in practical applications with a finite time-bandwidth product. Monte–Carlo simulations are conducted to verify the approximation and to quantify its accuracy and remaining errors. The findings are important for e.g. calibration or derivation of a device model in FMCW radar applications.

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Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential Inclusions

Symmetry ◽

10.3390/sym13010152 ◽

2021 ◽

Vol 13 (1) ◽

pp. 152

Author(s):

Mutti-Ur Rehman ◽

Sohail Iqbal ◽

Jehad Alzabut ◽

Rami Ahmad El-Nabulsi

Keyword(s):

Differential Equations ◽

Differential Inclusions ◽

Linear Time ◽

System Of Differential Equations ◽

Bounded Linear ◽

Linear Time Invariant ◽

Linear Differential Inclusions ◽

Linear Time Invariant Systems ◽

Linear Differential ◽

Time Invariant

In this article, we present a stability analysis of linear time-invariant systems in control theory. The linear time-invariant systems under consideration involve the diagonal norm bounded linear differential inclusions. We propose a methodology based on low-rank ordinary differential equations. We construct an equivalent time-invariant system (linear) and use it to acquire an optimization problem whose solutions are given in terms of a system of differential equations. An iterative method is then used to solve the system of differential equations. The stability of linear time-invariant systems with diagonal norm bounded differential inclusion is studied by analyzing the Spectrum of equivalent systems.

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