scholarly journals Asymptotic achievability for linear time invariant state space systems

2010 ◽  
Author(s):  
Harsh Vinjamoor ◽  
Arjan van der Schaft
Keyword(s):  
State Space ◽  
Linear Time ◽  
Space Systems ◽  
Invariant State ◽  
Linear Time Invariant ◽  
State Space Systems ◽  
Time Invariant

scholarly journals Explaining Savings for Visuomotor Adaptation: Linear Time-Invariant State-Space Models Are Not Sufficient

2008 ◽  
Vol 100 (5) ◽  
pp. 2537-2548 ◽  
Author(s):  
Eric Zarahn ◽  
Gregory D. Weston ◽  
Johnny Liang ◽  
Pietro Mazzoni ◽  
John W. Krakauer
Keyword(s):  
State Space ◽  
Linear Time ◽  
State Space Model ◽  
Visuomotor Adaptation ◽  
Invariant State ◽  
Visuomotor Rotation ◽  
Body Memory ◽  
Linear Time Invariant ◽  
And Coping ◽  
Time Invariant

Adaptation of the motor system to sensorimotor perturbations is a type of learning relevant for tool use and coping with an ever-changing body. Memory for motor adaptation can take the form of savings: an increase in the apparent rate constant of readaptation compared with that of initial adaptation. The assessment of savings is simplified if the sensory errors a subject experiences at the beginning of initial adaptation and the beginning of readaptation are the same. This can be accomplished by introducing either 1) a sufficiently small number of counterperturbation trials (counterperturbation paradigm [ CP]) or 2) a sufficiently large number of zero-perturbation trials (washout paradigm [ WO]) between initial adaptation and readaptation. A two-rate, linear time-invariant state-space model (SSMLTI,2) was recently shown to theoretically produce savings for CP. However, we reasoned from superposition that this model would be unable to explain savings for WO. Using the same task (planar reaching) and type of perturbation (visuomotor rotation), we found comparable savings for both CP and WO paradigms. Although SSMLTI,2 explained some degree of savings for CP it failed completely for WO. We conclude that for visuomotor rotation, savings in general is not simply a consequence of LTI dynamics. Instead savings for visuomotor rotation involves metalearning, which we show can be modeled as changes in system parameters across the phases of an adaptation experiment.

On krylov matrices and controllability of n-dimensional linear time-invariant state equations

1996 ◽  
Vol 3 (1-2) ◽  
pp. 99-109
Author(s):  
Andrzej Maćkiewicz ◽  
Francisco López Almansa ◽  
José A. Inaudi
Keyword(s):  
Linear Time ◽  
Invariant State ◽  
State Equations ◽  
Linear Time Invariant ◽  
Time Invariant

Application of Supervisory Predictive Control Based on T-S Model in pH Neutralization Process

2014 ◽  
Vol 511-512 ◽  
pp. 867-870
Author(s):  
Su Zhen Li ◽  
Xiang Jie Liu ◽  
Gang Yuan
Keyword(s):  
Predictive Control ◽  
Linear Time ◽  
Control Performance ◽  
Invariant State ◽  
Linear Time Invariant ◽  
Neutralization Process ◽  
S Model ◽  
Time Invariant ◽  
Ph Neutralization ◽  
Ph Neutralization Process

T-S model is linearized at sampling points into the form of linear time-invariant state space , and using supervisory predictive control and muti-step predictive control strategy, which reduces amount of calculation and improves the control performance. Introduction

Robust Controllability of Interval Fractional Order Linear Time Invariant Systems

2005 ◽  
Author(s):  
Yang Quan Chen ◽  
Hyo-Sung Ahn ◽  
Dingyu¨ Xue
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Linear Time ◽  
Interval Uncertainty ◽  
State Matrix ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Robust Controllability ◽  
Time Invariant

We consider uncertain fractional-order linear time invariant (FO-LTI) systems with interval coefficients. Our focus is on the robust controllability issue for interval FO-LTI systems in state-space form. We re-visited the controllability problem for the case when there is no interval uncertainty. It turns out that the stability check for FO-LTI systems amounts to checking the conventional integer order state space using the same state matrix A and the input coupling matrix B. Based on this fact, we further show that, for interval FO-LTI systems, the key is to check the linear dependency of a set of interval vectors. Illustrative examples are presented.

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