Estimation of Plasma Insulin Using Nonlinear Filtering

2007 ◽  
Author(s):  
Kiriakos Kiriakidis ◽  
Richard O’Brien
Keyword(s):  
Nonlinear Filtering ◽  
Plasma Insulin ◽  
Estimation Error ◽  
Nonlinear Filter ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Aggregate Model ◽  
Aggregate Modeling ◽  
The Stability

The glucose-insulin dynamics as captured by the standard (Bergman) model are both nonlinear and time-varying. To develop an insulin estimator (or filter), the authors use an aggregate model expansion of the nonlinear dynamics while treating the time-varying component of the model as an exogenous input. The aggregate model allows for the design of a particular nonlinear filter (or observer) that uses a weighted summation of constant feedback gains and admits a straightforward implementation. Furthermore, the aggregate modeling approach enables the stability analysis of the estimation error equation through linear matrix inequalities. The aggregate model insulin filter is compared with an existing insulin filter through numerical simulation.

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.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

Stabilization of the Rotary Inverted Pendulum Using Aggregate Modeling

2006 ◽  
Author(s):  
Kiriakos Kiriakidis ◽  
Matthew Feemster ◽  
Richard O'Brien
Keyword(s):  
Linear Matrix Inequalities ◽  
Inverted Pendulum ◽  
Feasibility Problem ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Aggregate Model ◽  
Stabilizing Controller ◽  
Aggregate Modeling ◽  
Operating Region ◽  
Rotary Inverted Pendulum

Using the method of aggregate modeling, the paper derives an approximation of the rotary pendulum's Euler-Lagrange dynamics within a specified operating region. Based on the resulting aggregate model, the authors cast the system's stabilization as a feasibility problem associated with linear matrix inequalities. Furthermore, the authors test the resulting stabilizing controller on the actual rotary pendulum and verify the expected results experimentally.

Nonlinear State Estimation Using Aggregate Modeling

2007 ◽  
Author(s):  
Kiriakos Kiriakidis ◽  
Matthew Feemster ◽  
Richard T. O’Brien
Keyword(s):  
State Estimation ◽  
Estimation Error ◽  
The State ◽  
Linear Feedback ◽  
Aggregate Model ◽  
Nonlinear State Estimation ◽  
Aggregate Modeling ◽  
Error Dynamics ◽  
The Stability ◽  
Nonlinear State

The paper addresses the state estimation problem for a general class of nonlinear systems. Using an expansion of nonlinear drift dynamics in terms of an aggregate model, the authors analyze the stability of the estimation error equation. Although the treatment is limited to linear feedback, the method results in quadratically stable error dynamics inside a large subset of the state space. The authors tested and verified the proposed approach on the nonlinear dynamics of the rotary pendulum.

scholarly journals Improved Criteria on Delay-Dependent Stability for Discrete-Time Neural Networks with Interval Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
O. M. Kwon ◽  
M. J. Park ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Lyapunov Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Interval Time ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

The purpose of this paper is to investigate the delay-dependent stability analysis for discrete-time neural networks with interval time-varying delays. Based on Lyapunov method, improved delay-dependent criteria for the stability of the networks are derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii functional and utilizing reciprocally convex approach. Also, a new activation condition which has not been considered in the literature is proposed and utilized for derivation of stability criteria. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Fuzzy Control of a Class of Discrete-Time Fuzzy Bilinear Systems with Time-Delay

2012 ◽  
Vol 482-484 ◽  
pp. 1881-1885
Author(s):  
Jian Hu Jiang ◽  
Chao Wu ◽  
Yun Wang Ge ◽  
Li Jun Song
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Bilinear System ◽  
Stability Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

The stability control problem is considered for a class of discrete-time T-S fuzzy bilinear system with time-varying delay in both state and input. Based on the parallel distribute compensation (PDC) scheme, some sufficient conditions are derived to guarantee the global asymptotically stability of the overall fuzzy system, which are represented in terms of matrix inequality. The corresponding controller can be obtained by solving a set of linear matrix inequalities. Finally, a simulation example shows that the approach is effective.

Robust Absolute Stability Criteria for Uncertain Lurie System With Interval Time-Varying Delay

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Pankaj Mukhija ◽  
Indra Narayan Kar ◽  
Rajendra K. P. Bhatt
Keyword(s):  
Absolute Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Interval Time ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
Chua’S Oscillator ◽  
The Stability ◽  
Varying Delay

This paper addresses the problem of absolute stability of Lurie system with interval time-varying delay. The delay range is divided into two equal segments and an appropriate Lyapunov–Krasovskii functional (LKF) is defined. A tighter bounding technique for the derivative of LKF is developed. This bounding technique in combination with the Wirtinger inequality is used to develop the absolute stability criterion in terms of linear matrix inequalities (LMIs). The stability analysis is also extended to the Lurie system with norm-bounded parametric uncertainties. The effectiveness of the proposed approach has been illustrated through a numerical example and Chua's oscillator.

scholarly journals Robust Exponential Stability Criteria of LPD Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Kanit Mukdasai ◽  
Akkharaphong Wongphat ◽  
Piyapong Niamsup
Keyword(s):  
Exponential Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Robust Exponential Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Parameter Dependent

This paper investigates the problem of robust exponential stability for linear parameter-dependent (LPD) systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Sensor fault and state estimation for uncertain fuzzy descriptor systems: An LMI approach

2018 ◽  
Vol 41 (1) ◽  
pp. 135-144 ◽  
Author(s):  
Imen Haj Brahim ◽  
Driss Mehdi ◽  
Mohamed Chaabane
Keyword(s):  
State Estimation ◽  
Linear Matrix Inequalities ◽  
Estimation Error ◽  
External Disturbance ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Matrix Inequalities ◽  
Sensor Fault ◽  
The Stability

This paper deals with the problem of robust sensor fault diagnosis of Takagi–Sugeno fuzzy uncertain descriptor systems affected by bounded external disturbance with unmeasurable premise variables. This problem is solved using a descriptor approach to easily convert the stability conditions into linear matrix inequalities). By augmenting the sensor fault into a state vector, a fuzzy descriptor observer is constructed to simultaneously estimate the state and sensor faults and attenuate the effect of both modelling uncertainties and external disturbance on the estimation error. The faults affecting the system behaviour are considered as an auxiliary state variable. Based on the Lyapunov theory and [Formula: see text] technique, two different approaches are proposed to study the convergence of the state estimation error and the stability conditions are given in terms of linear matrix inequalities. Finally, an application to a model of rolling disk is given to show the applicability of the proposed approaches.

Dissipativity analysis of delayed stochastic generalized neural networks with Markovian jump parameters

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Grienggrai Rajchakit ◽  
Ramalingam Sriraman ◽  
Rajendran Samidurai
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stochastic Perturbations ◽  
Practical Applications ◽  
Markovian Jump Parameters ◽  
Generalized Neural Networks ◽  
System Information ◽  
Dissipativity Analysis

Abstract This article discusses the dissipativity analysis of stochastic generalized neural network (NN) models with Markovian jump parameters and time-varying delays. In practical applications, most of the systems are subject to stochastic perturbations. As such, this study takes a class of stochastic NN models into account. To undertake this problem, we first construct an appropriate Lyapunov–Krasovskii functional with more system information. Then, by employing effective integral inequalities, we derive several dissipativity and stability criteria in the form of linear matrix inequalities that can be checked by the MATLAB LMI toolbox. Finally, we also present numerical examples to validate the usefulness of the results.

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