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

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
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.

DISSIPATIVE DYNAMICAL SYSTEMS IN A BEHAVIORAL CONTEXT

1991 ◽  
Vol 01 (01) ◽  
pp. 1-25 ◽  
Author(s):  
SIEP WEILAND ◽  
JAN C. WILLEMS
Keyword(s):  
Dynamical Systems ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Dissipative System ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Dissipative Dynamical Systems ◽  
Necessary And Sufficient ◽  
Lq Theory ◽  
Time Invariant

Various conceptual definitions of dissipativeness of time invariant dynamical systems are introduced. A formal distinction is made between external and internal dissipativeness and it is shown that, under certain conditions, these notions are equivalent. A characterization of the class of internal storage functions associated with a dissipative system is given. The results are applied to the class of finite-dimensional linear time invariant systems. Necessary and sufficient conditions for dissipativeness of systems in this class are derived and the relation to LQ-theory is discussed.

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

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Damiano Zanotto ◽  
Giulio Rosati ◽  
Sunil K. Agrawal
Keyword(s):  
Differential Equations ◽  
Dynamic Optimization ◽  
Linear Time ◽  
Traditional Approach ◽  
Linear Time Invariant ◽  
System P ◽  
Lti System ◽  
Higher Order Method ◽  
Linear Time Invariant Systems ◽  
Time Invariant

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.

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

Symmetry ◽  
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.

scholarly journals Positivity and Stability of the Solutions of Caputo Fractional Linear Time-Invariant Systems of Any Order with Internal Point Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-25 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Dynamic Systems ◽  
Linear Time ◽  
Asymptotic Properties ◽  
Linear Time Invariant ◽  
Nonnegative Solutions ◽  
Fractional Differential ◽  
Linear Time Invariant Systems ◽  
The Stability ◽  
Time Invariant ◽  
Point Delays

This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained results are independent of the sizes of the delays.

Enhancing Controllability and Observability in Underactuated and Undersensed Systems Through Switching: Application to Vibration Control

2004 ◽  
Vol 126 (4) ◽  
pp. 790-799 ◽  
Author(s):  
Shahin S. Nudehi ◽  
Ranjan Mukherjee
Keyword(s):  
Dynamical Systems ◽  
Vibration Suppression ◽  
Linear Time ◽  
Flexible Beam ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Controllability And Observability ◽  
Time Invariant ◽  
Control Designs

Many dynamical systems use transducers that can function both as actuators and sensors. It is possible to continuously switch the functionality of the transducer elements in such systems and effectively use each element both as an actuator and a sensor. This provides the scope for significantly reducing the number of transducer elements required for complete controllability and observability of the system and hence reduce the hardware required for controlled system operation. In this paper we advocate underactuation and undersensing in dynamical systems with the objective of reducing cost, weight, and system complexity. To this end, we first illustrate the role of switching in enhancing controllability and observability in underactuated and undersensed linear time-invariant systems and determine the switching requirement for observer-based control designs. For a proof of principle, we consider the problem of vibration suppression in a flexible beam instrumented with piezoelectric transducers. Using simulation and experiments, we demonstrate feasibility of switching the piezoelectric elements between actuator and sensor modalities and establish the merit of introducing underactuation and undersensing deliberately.

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