A direct solution to the linear variance equation of a time-invariant linear system

1969 ◽  
Vol 14 (5) ◽  
pp. 592-593 ◽  
Author(s):  
H. Rome
Keyword(s):  
Linear System ◽  
Direct Solution ◽  
Variance Equation ◽  
Time Invariant

On the modeling of linear system input stochastic processes with given accuracy and reliability

2018 ◽  
Vol 24 (2) ◽  
pp. 129-137
Author(s):  
Iryna Rozora ◽  
Mariia Lyzhechko
Keyword(s):  
Banach Space ◽  
Stochastic Process ◽  
Linear System ◽  
Stochastic Processes ◽  
Impulse Response Function ◽  
Output Process ◽  
Gaussian Stochastic Process ◽  
System Input ◽  
Time Invariant ◽  
Gaussian Stochastic Processes

AbstractThe paper is devoted to the model construction for input stochastic processes of a time-invariant linear system with a real-valued square-integrable impulse response function. The processes are considered as Gaussian stochastic processes with discrete spectrum. The response on the system is supposed to be an output process. We obtain the conditions under which the constructed model approximates a Gaussian stochastic process with given accuracy and reliability in the Banach space{C([0,1])}, taking into account the response of the system. For this purpose, the methods and properties of square-Gaussian processes are used.

Accelerated Direct Solution of the Method-of-Moments Linear System

2013 ◽  
Vol 101 (2) ◽  
pp. 364-371 ◽  
Author(s):  
A. Heldring ◽  
J. M. Tamayo ◽  
E. Ubeda ◽  
J. M. Rius
Keyword(s):  
Linear System ◽  
Method Of Moments ◽  
Direct Solution

Pole Placement for Single-Input Linear System by Proportional-Derivative State Feedback

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Taha H. S. Abdelaziz
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
State Feedback ◽  
Pole Placement ◽  
Feedback Gain ◽  
Time Varying ◽  
Placement Problem ◽  
Single Input ◽  
Time Invariant

This paper deals with the direct solution of the pole placement problem for single-input linear systems using proportional-derivative (PD) state feedback. This problem is always solvable for any controllable system. The explicit parametric expressions for the feedback gain controllers are derived which describe the available degrees of freedom offered by PD state feedback. These freedoms are utilized to obtain closed-loop systems with small gains. Its derivation is based on the transformation of linear system into control canonical form by a special coordinate transformation. The solving procedure results into a formula similar to Ackermann’s one. In the present work, both time-invariant and time-varying linear systems are treated. The effectiveness of the proposed method is demonstrated by the simulation examples of both time-invariant and time-varying systems.

scholarly journals Rapid SINS Two-Position Ground Alignment Scheme Based on Piecewise Combined Kalman Filter and Azimuth Constraint Information

Sensors ◽  
2019 ◽  
Vol 19 (5) ◽  
pp. 1125 ◽  
Author(s):  
Lu Zhang ◽  
Wenqi Wu ◽  
Maosong Wang
Keyword(s):  
Kalman Filter ◽  
Linear System ◽  
State Estimation ◽  
Rate Of Convergence ◽  
Inertial Navigation System ◽  
Alignment Algorithm ◽  
Time Consumption ◽  
Performance Factors ◽  
Constraint Information ◽  
Time Invariant

The accuracy and rate of convergence are two important performance factors for initial ground alignment of a strapdown inertial navigation system (SINS). For navigation-grade SINS, gyro biases and accelerometer offsets can be modeled as constant values during the alignment period, and they can be calibrated through two-position ground alignment schemes. In many situations for SINS ground alignment, the azimuth of the vehicle remains nearly constant. This quasi-stationary alignment information can be used as an augmented measurement. In this paper, a piecewise combined Kalman filter utilizing relative azimuth constraint (RATP) is proposed to improve the alignment precision and to reduce the time consumption for error convergence. It is presented that a piecewise time-invariant linear system can be combined into a whole extended time-invariant linear system so that a piecewise combined Kalman filter can be designed for state estimation. A two-position ground alignment algorithm for SINS is designed based on the proposed piecewise combined Kalman filter. Numerical simulations and experimental results show its superiority to the conventional algorithms in terms of accuracy and the rate of convergence.

KETEROBSERVASIAN SISTEM LINIER DISKRIT

2015 ◽  
Vol 4 (1) ◽  
pp. 108
Author(s):  
Midian Manurung
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
State Vector ◽  
The State ◽  
Input Vector ◽  
Linear Control ◽  
Time Interval ◽  
Initial State ◽  
Time Invariant ◽  
Time Linear

Given the following discrete time-invariant linear control systems:where x 2 Rnx(t + 1) = Ax(t) + Bu(t);y(t) = Cx(t);is the state vector, u 2 Rmis an input vector, y 2 Rris dened as anoutput, A 2 Rnn, B 2 Rnm, and t 2 Zis dened as time. Linear system is said to beobservable on the nite time interval [t0; t+f] if any initial state xis uniquely determinedby the output y(t) over the same time interval. In order to examine the observabilityof the system, we will use a criteria, that is by determining the observability Gramianmatrix of the system is nonsingular and rank of the observability matrix for the systemis n.

Optimal Observer Design With Specified Eigenvalues for Time-Invariant Linear System

1980 ◽  
Vol 102 (3) ◽  
pp. 148-150 ◽  
Author(s):  
F. C. Kung ◽  
Y. M. Yeh
Keyword(s):  
Linear System ◽  
Design Methods ◽  
Observer Design ◽  
Block Pulse Functions ◽  
Estimate Error ◽  
Time Invariant

The elements of the observer matrix are determined to meet the specified eigenvalues, distinct and multiple, and at the same time, the measure of quadratic estimate error expressed in block pulse functions is minimized. It is relatively simple as compared to other design methods for optimal observers.

Globally Feedback Linearizable Time-Invariant Systems: Optimal Solution for Mayer’s Problem

1998 ◽  
Vol 122 (2) ◽  
pp. 343-347 ◽  
Author(s):  
M. Schlemmer ◽  
S. K. Agrawal
Keyword(s):  
Optimal Solution ◽  
Point Boundary ◽  
Direct Solution ◽  
Alternate Form ◽  
Input System ◽  
Time Problem ◽  
Single Input ◽  
Actuator Constraints ◽  
Time Invariant ◽  
Minimum Time Problem

This paper discusses the optimal solution of Mayer’s problem for globally feedback linearizable time-invariant systems subject to general nonlinear path and actuator constraints. This class of problems includes the minimum time problem, important for engineering applications. Globally feedback linearizable nonlinear systems are diffeomorphic to linear systems that consist of blocks of integrators. Using this alternate form, it is proved that the optimal solution always lies on a constraint arc. As a result of this optimal structure of the solution, efficient numerical procedures can be developed. For a single input system, this result allows to characterize and build the optimal solution. The associated multi-point boundary value problem is then solved using direct solution techniques. [S0022-0434(00)02002-5]

scholarly journals Fast Direct Solution of Method of Moments Linear System

2007 ◽  
Vol 55 (11) ◽  
pp. 3220-3228 ◽  
Author(s):  
Alex Heldring ◽  
Juan. M. Rius ◽  
JosÉ Maria Tamayo ◽  
Josep Parron ◽  
Eduard Ubeda
Keyword(s):  
Linear System ◽  
Method Of Moments ◽  
Direct Solution
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