scholarly journals A Modified Stability Analysis of Two-Dimensional Linear Time Invariant Discrete Systems within the Unity-Shifted Unit Circle

2016 ◽  
Vol 07 (03) ◽  
pp. 110-118
Author(s):  
Periyasamy Ramesh
Keyword(s):  
Stability Analysis ◽  
Unit Circle ◽  
Linear Time ◽  
Discrete Systems ◽  
Two Dimensional ◽  
Linear Time Invariant ◽  
Time Invariant

Linear Approximations for Swing Leg Motion During Gait

1984 ◽  
Vol 106 (2) ◽  
pp. 137-143 ◽  
Author(s):  
W. H. Lee ◽  
J. M. Mansour
Keyword(s):  
Linear Systems ◽  
System Analysis ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
State Variables ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Leg Motion ◽  
Time Invariant

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

Stabilization and Optimal Quadratic Regulation of Linear Time-Invariant Discrete Systems with Data Dropout Compensation

2013 ◽  
Vol 816-817 ◽  
pp. 574-582
Author(s):  
Manuel de La Sen ◽  
S. Alonso-Quesada ◽  
A. Ibeas
Keyword(s):  
Linear Time ◽  
Finite Size ◽  
Discrete Systems ◽  
Memory Storage ◽  
Control Structures ◽  
Global Asymptotic Stabilization ◽  
Linear Time Invariant ◽  
Transmission Errors ◽  
Remote Controller ◽  
Time Invariant

This paper discusses the global asymptotic stabilization and least-squares optimal control for a linear system with potential transmission errors subject to Bernouilli statistics from a remote controller to the actuator. The controlled system is able to compensate certain missed data through the use of finite size fixed memory storage arrays which store the last valid data which has been transmitted so as to replace the current missed one in the control structures.

scholarly journals Modified Schur-Cohn Criterion for Stability of Delayed Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Juan Ignacio Mulero-Martínez
Keyword(s):  
Linear Time ◽  
Discrete Systems ◽  
Delayed Systems ◽  
Triangular Matrices ◽  
Numerical Errors ◽  
Real Roots ◽  
Linear Time Invariant ◽  
Alternative Approach ◽  
Linear Time Invariant Systems ◽  
Time Invariant

A modified Schur-Cohn criterion for time-delay linear time-invariant systems is derived. The classical Schur-Cohn criterion has two main drawbacks; namely, (i) the dimension of the Schur-Cohn matrix generates some round-off errors eventually resulting in a polynomial ofswith erroneous coefficients and (ii) imaginary roots are very hard to detect when numerical errors creep in. In contrast to the classical Schur-Cohn criterion an alternative approach is proposed in this paper which is based on the application of triangular matrices over a polynomial ring in a similar way as in the Jury test of stability for discrete systems. The advantages of the proposed approach are that it halves the dimension of the polynomial and it only requires seeking real roots, making this modified criterion comparable to the Rekasius substitution criterion.

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