New approach for the stability analysis of linear time-varying state-space models

1991 ◽  
Vol 22 (7) ◽  
pp. 1315-1319
Author(s):  
JOHN J. H. CHOU
Keyword(s):  
Stability Analysis ◽  
State Space ◽  
Linear Time ◽  
State Space Models ◽  
Time Varying ◽  
New Approach ◽  
The Stability

scholarly journals JOINT ESTIMATION OF STATES AND PARAMETERS OF LINEAR SYSTEMS WITH PARAMETER FAULTS UNDER NON-GAUSSIAN NOISES

2020 ◽  
Vol 18 (2) ◽  
pp. 113
Author(s):  
Vladimir Stojanović ◽  
Dragan Pršić ◽  
Ljubiša Dubonjić
Keyword(s):  
State Space ◽  
Stochastic Systems ◽  
Fault Tolerant ◽  
Linear Time ◽  
Practical Importance ◽  
Joint Estimation ◽  
State Space Models ◽  
Time Varying ◽  
Linear State ◽  
Non Gaussian

Joint estimation of states and time-varying parameters of linear state space models is of practical importance for the fault diagnosis and fault tolerant control. Previous works on this topic consider the joint estimation in the Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of the joint parameter-state robust estimation of linear state space models in the presence of non-Gaussian noises. The case of parameter-dependent matrices is considered. Because of its good features in robust filtering, the extended Masreliez-Martin filter represents a cornerstone for realization of the robust algorithms for joint state-parameter estimation of linear time-varying stochastic systems in the presence of non-Gaussian noises. The good features of the proposed robust algorithm for joint estimation of linear time-varying stochastic systems are illustrated by intensive simulations.

scholarly journals Linear time-varying Luenberger observer applied to diabetes

2017 ◽  
Author(s):  
Onofre Orozco López ◽  
Carlos Eduardo Castañeda Hernández ◽  
Agustín Rodríguez Herrero ◽  
Gema García Saéz ◽  
María Elena Hernando
Keyword(s):  
State Space ◽  
Linear Time ◽  
Time Varying ◽  
Data Set ◽  
Luenberger Observer ◽  
Meal Plan ◽  
The Stability ◽  
Real Patients ◽  
Selection Of

We present a linear time-varying Luenberger observer (LTVLO) using compartmental models to estimate the unmeasurable states in patients with type 1 diabetes. The LTVLO proposed is based on the linearization in an operation point of the virtual patient (VP), where a linear time-varying system is obtained. LTVLO gains are obtained by selection of the asymptotic eigenvalues where the observability matrix is assured. The estimation of the unmeasurable variables is done using Ackermann's methodology. Additionally, it is shown the Lyapunov approach to prove the stability of the time-varying proposal. In order to evaluate the proposed methodology, we designed three experiments: A) VP obtained with the Bergman minimal model; B) VP obtained with the compartmental model presented by Hovorka in 2004; and C) real patients data set. For experiments A) and B), it is applied a meal plan to the VP, where the dynamic response of each state model is compared to the response of each variable of the time-varying observer. Once the observer is evaluated in experiment B), the proposal is applied to experiment C) with data extracted from real patients and the unmeasurable state space variables are obtained with the LTVLO. LTVLO methodology has the feature of being updated each instant of time to estimate the states under a known structure. The results are obtained using simulation with MatlabTM and SimulinkTM. The LTVLO estimates the unmeasurable states from in silico patients with high accuracy by means of the update of Luenberger gains at each iteration. The accuracy of the estimated state space variables is validated through fit parameter.

scholarly journals Linear time-varying Luenberger observer applied to diabetes

2017 ◽  
Author(s):  
Onofre Orozco López ◽  
Carlos Eduardo Castañeda Hernández ◽  
Agustín Rodríguez Herrero ◽  
Gema García Saéz ◽  
María Elena Hernando
Keyword(s):  
State Space ◽  
Linear Time ◽  
Time Varying ◽  
Data Set ◽  
Luenberger Observer ◽  
Meal Plan ◽  
The Stability ◽  
Real Patients ◽  
Selection Of

We present a linear time-varying Luenberger observer (LTVLO) using compartmental models to estimate the unmeasurable states in patients with type 1 diabetes. The LTVLO proposed is based on the linearization in an operation point of the virtual patient (VP), where a linear time-varying system is obtained. LTVLO gains are obtained by selection of the asymptotic eigenvalues where the observability matrix is assured. The estimation of the unmeasurable variables is done using Ackermann's methodology. Additionally, it is shown the Lyapunov approach to prove the stability of the time-varying proposal. In order to evaluate the proposed methodology, we designed three experiments: A) VP obtained with the Bergman minimal model; B) VP obtained with the compartmental model presented by Hovorka in 2004; and C) real patients data set. For experiments A) and B), it is applied a meal plan to the VP, where the dynamic response of each state model is compared to the response of each variable of the time-varying observer. Once the observer is evaluated in experiment B), the proposal is applied to experiment C) with data extracted from real patients and the unmeasurable state space variables are obtained with the LTVLO. LTVLO methodology has the feature of being updated each instant of time to estimate the states under a known structure. The results are obtained using simulation with MatlabTM and SimulinkTM. The LTVLO estimates the unmeasurable states from in silico patients with high accuracy by means of the update of Luenberger gains at each iteration. The accuracy of the estimated state space variables is validated through fit parameter.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

A new approach to the stability analysis of thawing slopes

1980 ◽  
Vol 17 (4) ◽  
pp. 607-612 ◽  
Author(s):  
Luis E. Vallejo
Keyword(s):  
Stability Analysis ◽  
Water Content ◽  
Pore Water ◽  
Active Layer ◽  
Necessary Conditions ◽  
Mass Movements ◽  
New Approach ◽  
Pore Water Pressures ◽  
The Stability ◽  
Excess Pore

A new approach to the stability analysis of thawing slopes at shallow depths, taking into consideration their structure (this being a mixture of hard crumbs of soil and a fluid matrix), is presented. The new approach explains shallow mass movements such as skin flows and tongues of bimodal flows, which usually take place on very low slope inclinations independently of excess pore water pressures or increased water content in the active layer, which are necessary conditions in the methods available to date to explain these movements.

scholarly journals Delayed Trilateral Teleoperation of a Mobile Robot

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
D. Santiago ◽  
E. Slawiñski ◽  
V. Mut
Keyword(s):  
Stability Analysis ◽  
Mobile Robot ◽  
Shared Environment ◽  
Time Varying ◽  
Control Parameters ◽  
Simple Test ◽  
Control Loop ◽  
Teleoperation System ◽  
Human Operators ◽  
The Stability

This paper analyzes the stability of a trilateral teleoperation system of a mobile robot. This type of system is nonlinear, time-varying, and delayed and includes a master-slave kinematic dissimilarity. To close the control loop, three P+d controllers are used under a position master/slave velocity strategy. The stability analysis is based on Lyapunov-Krasovskii theory where a functional is proposed and analyzed to get conditions for the control parameters that assure a stable behavior, keeping the synchronism errors bounded. Finally, the theoretical result is verified in practice by means of a simple test, where two human operators both collaboratively and simultaneously drive a 3D simulator of a mobile robot to achieve an established task on a remote shared environment.

New Method for the Stability Analysis of Neutral Systems with Time-Varying Structured Uncertainties

2018 ◽  
Author(s):  
Liming Ding ◽  
Dajiang He ◽  
Xianwu Mi ◽  
Jun Shu ◽  
Leiping Chen ◽  
...  
Keyword(s):  
Stability Analysis ◽  
New Method ◽  
Time Varying ◽  
Neutral Systems ◽  
The Stability
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