scholarly journals Input retrieval in finite dimensional linear systems

1982 ◽  
Vol 23 (4) ◽  
pp. 357-382 ◽  
Author(s):  
P. G. Howlett
Keyword(s):  
Linear Systems ◽  
Type System ◽  
System Matrix ◽  
Fundamental Idea ◽  
Finite Dimensional ◽  
First Case ◽  
Direct Linkage ◽  
Explicit Formulae ◽  
Output Only ◽  
General Method

AbstractFor finite dimensional linear systems it is known that in certain circumstances the input can be retrieved from a knowledge of the output only. The main aim of this paper is to produce explicit formulae for input retrieval in systems which do not possess direct linkage from input to output. Although two different procedures are suggested the fundamental idea in both cases is to find an expression for the inverse transfer function of the system. In the first case this is achieved using a general method of power series inversion and in the second case by a sequence of elementary operations on a Rosenbrock type system matrix.

scholarly journals General methods of convergence and summability

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Francisco Javier García-Pacheco ◽  
Ramazan Kama ◽  
María del Carmen Listán-García
Keyword(s):  
Geometric Structure ◽  
Banach Limit ◽  
Limit Operator ◽  
Finite Dimensional ◽  
Free Ultrafilter ◽  
General Method

AbstractThis paper is on general methods of convergence and summability. We first present the general method of convergence described by free filters of $\mathbb{N} $ N and study the space of convergence associated with the filter. We notice that $c(X)$ c ( X ) is always a space of convergence associated with a filter (the Frechet filter); that if X is finite dimensional, then $\ell _{\infty }(X)$ ℓ ∞ ( X ) is a space of convergence associated with any free ultrafilter of $\mathbb{N} $ N ; and that if X is not complete, then $\ell _{\infty }(X)$ ℓ ∞ ( X ) is never the space of convergence associated with any free filter of $\mathbb{N} $ N . Afterwards, we define a new general method of convergence inspired by the Banach limit convergence, that is, described through operators of norm 1 which are an extension of the limit operator. We prove that $\ell _{\infty }(X)$ ℓ ∞ ( X ) is always a space of convergence through a certain class of such operators; that if X is reflexive and 1-injective, then $c(X)$ c ( X ) is a space of convergence through a certain class of such operators; and that if X is not complete, then $c(X)$ c ( X ) is never the space of convergence through any class of such operators. In the meantime, we study the geometric structure of the set $\mathcal{HB}(\lim ):= \{T\in \mathcal{B} (\ell _{\infty }(X),X): T|_{c(X)}= \lim \text{ and }\|T\|=1\}$ HB ( lim ) : = { T ∈ B ( ℓ ∞ ( X ) , X ) : T | c ( X ) = lim  and  ∥ T ∥ = 1 } and prove that $\mathcal{HB}(\lim )$ HB ( lim ) is a face of $\mathsf{B} _{\mathcal{L}_{X}^{0}}$ B L X 0 if X has the Bade property, where $\mathcal{L}_{X}^{0}:= \{ T\in \mathcal{B} (\ell _{\infty }(X),X): c_{0}(X) \subseteq \ker (T) \} $ L X 0 : = { T ∈ B ( ℓ ∞ ( X ) , X ) : c 0 ( X ) ⊆ ker ( T ) } . Finally, we study the multipliers associated with series for the above methods of convergence.

The Methods to Study the Influence of the Clearance in the Case of Great Speeds and Small Speeds

2013 ◽  
Vol 837 ◽  
pp. 88-92
Author(s):  
Jan Cristian Grigore
Keyword(s):  
Dynamic Behavior ◽  
Reaction Force ◽  
Accurate Method ◽  
Angular Speed ◽  
Connecting Rod ◽  
Lagrange Equations ◽  
Joint Rotation ◽  
First Case ◽  
Multi Body ◽  
General Method

In kinematic couplings, clearances are inevitable for their operation. The size of these clearances but as a consequence of use, causes a malfunction of the mechanism to which it belongs. The law of motion of driveline changes, big clearances, non-technological system causes vibration, leading to discomfort, uncertainty, and thus reach its degradation. In the paper we shall make a few of geometric and mechanical type considerations about the clearances in the linkages, linkages planes with joint rotation links. Based on mathematical algorithm developed and applied crank mechanism, the model presented in [1], this paper scientifically developed mathematical model, proposing mathematical models to study the influence of the size of the clearance in general dynamic calculation mechanisms. Mechanism considered is crank connecting rod mechanism with clearance cinematic coupling between rod and crank rotation. The paper makes a study of the influence on the dynamic behavior of the crank rod mechanism at high speeds, but also general method algorithm is developed and accurate method to assess the dynamic behavior of multi-body mechanism. The first case is considered a constant angular speed motor and thus determine the elemental expressions that establish the mechanism position, velocity and acceleration expressions in the two directions heads elements. Finally we obtain the expression of the normal reaction force, as well as position expression that defines its angle. With reaction force can specify phase (contact, flight, impact) [1], the behavior of the journal. For the case of general method - the method multi-body - the exact method are established liaison relationships between the parameters , write matrices , inertia matrix. Use Lagrange equations, if non-holonomic constraints. Matrix differential equation of motion is written and it can be solved numerically using Runge-Kutta method of order four. Of the iterative method, we obtain the parameters used in calculating the reaction force expression that can be evaluated accurately in journal bearings behaviour. Any would be their source of appearance, they usually produce unwished effects during the mechanisms functioning.

Alternating projections and interpolation of stationary processes

1992 ◽  
Vol 29 (4) ◽  
pp. 921-931 ◽  
Author(s):  
Mohsen Pourahmadi
Keyword(s):  
Missing Values ◽  
Stationary Process ◽  
Dimensional Space ◽  
Stationary Processes ◽  
Finite Dimensional Space ◽  
Alternating Projections ◽  
Von Neumann ◽  
Finite Dimensional ◽  
Explicit Formulae ◽  
Linear Interpolator

By using the alternating projection theorem of J. von Neumann, we obtain explicit formulae for the best linear interpolator and interpolation error of missing values of a stationary process. These are expressed in terms of multistep predictors and autoregressive parameters of the process. The key idea is to approximate the future by a finite-dimensional space.

Predictor Feedback of Uncertain Single-Input Systems

2020 ◽  
pp. 235-266
Author(s):  
Yang Zhu ◽  
Miroslav Krstic
Keyword(s):  
Output Feedback ◽  
State Feedback ◽  
System Matrix ◽  
Unknown Parameters ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Linear Plant ◽  
Single Input ◽  
Distributed Actuator

This chapter presents the predictor feedback for uncertain single-input systems. This is based on the predictor feedback framework for uncertainty-free single-input systems in the previous chapter. The chapter addresses the five combinations of the five uncertainties that come from a single-input linear plant with distributed actuator delay. These uncertainties include the following types: unknown delay, unknown delay kernel, unknown parameters in the system matrix, unmeasurable finite-dimensional plant state, and unmeasurable infinite-dimensional actuator state. The chapter then studies adaptive state feedback under unknown delay, delay kernel, and parameter. It also assesses robust output feedback under unknown delay, delay kernel, and PDE or ODE state.

scholarly journals Preconditioning for Sparse Linear Systems at the Dawn of the 21st Century: History, Current Developments, and Future Perspectives

2012 ◽  
Vol 2012 ◽  
pp. 1-49 ◽  
Author(s):  
Massimiliano Ferronato
Keyword(s):  
Linear Systems ◽  
Specific Problem ◽  
General Purpose ◽  
Sparse Linear Systems ◽  
System Matrix ◽  
Preconditioning Techniques ◽  
Key Factor ◽  
Recent Developments ◽  
Approximate Inverses ◽  
Linear Systems Of Equations

Iterative methods are currently the solvers of choice for large sparse linear systems of equations. However, it is well known that the key factor for accelerating, or even allowing for, convergence is the preconditioner. The research on preconditioning techniques has characterized the last two decades. Nowadays, there are a number of different options to be considered when choosing the most appropriate preconditioner for the specific problem at hand. The present work provides an overview of the most popular algorithms available today, emphasizing the respective merits and limitations. The overview is restricted to algebraic preconditioners, that is, general-purpose algorithms requiring the knowledge of the system matrix only, independently of the specific problem it arises from. Along with the traditional distinction between incomplete factorizations and approximate inverses, the most recent developments are considered, including the scalable multigrid and parallel approaches which represent the current frontier of research. A separate section devoted to saddle-point problems, which arise in many different applications, closes the paper.

scholarly journals HIGHER-ORDER SLIDING MODE DYNAMICS DESIGN FOR A CLASS OF SINGLE-INPUT LINEAR SYSTEMS

2020 ◽  
Vol 19 (2) ◽  
pp. 103
Author(s):  
Boban Veselić
Keyword(s):  
Linear Systems ◽  
Sliding Mode ◽  
Higher Order ◽  
System Matrix ◽  
Sliding Manifold ◽  
Single Input ◽  
Digital Simulations ◽  
Specific Sliding ◽  
Sliding Mode Dynamics ◽  
Mode Order

The paper considers a higher-order sliding mode dynamics design in a class of single-input linear systems having the invertible system matrix. The proposed sliding manifold selection method simultaneously provides a necessary relative degree of the sliding variable for a specific sliding mode order and the desired system dynamics after establishing that sliding mode. It is shown that the found unique solution satisfies these requirements. The theoretically obtained result is validated through a numerical example and illustrated by digital simulations.

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