Discrete-time Inversion Model Control of a Double-damper System with Uncertain Parameters

2017 ◽  
Vol 6 (3) ◽  
pp. 168
Author(s):  
Marwa Hannachi ◽  
Ikbel Bencheikh Ahmed ◽  
Dhaou Soudani
Keyword(s):  
Discrete Time ◽  
Algebraic Approach ◽  
Building Blocks ◽  
Internal Model Control ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Inversion ◽  
Time Model ◽  
Model Control ◽  
The Stability

<span>This paper addresses the control at discrete time of physical complex systems multi-inputs multi-outputs with variables parameters. Classified among the robust control laws the Internal Model Control (IMC) is adopted in this work to ensure the desired performances adjacent to the complexities of the system. However, the application of this control strategy requires that these different building blocks be open loop stable, which invites us, on the one hand, to apply the algebraic approach of Kharitinov for delimiting the summits stability domain’s system. On the other case, the Linear Matrix Inequalities (LMI) approach is applied to determine the corrector’s stability conditions obtained by a specific inversion of the chosen model. It is in this sense that we contribute by this work to execute the command by inversion the discrete-time model in order to ensure the stability and to maintain the performances the stability conditions of required for the double damper system with variable parameters.</span>

An Internal Model Control Based Static Anti-Windup Scheme With Improved Performance

2010 ◽  
Author(s):  
Wei Wu
Keyword(s):  
Internal Model ◽  
Input Saturation ◽  
Internal Model Control ◽  
Controller Synthesis ◽  
Linear Matrix ◽  
Constrained System ◽  
Stability Robustness ◽  
Model Control ◽  
Improved Performance ◽  
The Stability

This paper considers the synthesis of static anti-windup (AW) compensation within the internal model control (IMC) AW framework for stable plants subject to input saturation. Built on the conventional IMC AW scheme which preserves the stability and the stability robustness of the unconstrained system, the proposed static AW compensation improves the constrained system performance. L2 gain performance of the constrained system is considered for the static AW controller synthesis, resulting in a linear matrix inqualitiy. The effectiveness of this AW scheme is demonstrated by comparison with two AW methods from the literature through using two numerical examples.

ROBUST STABILITY, STABILISATION AND H-INFINITY CONTROL FOR PREMIUM-RESERVE MODELS IN A MARKOVIAN REGIME SWITCHING DISCRETE-TIME FRAMEWORK

2016 ◽  
Vol 46 (3) ◽  
pp. 747-778 ◽  
Author(s):  
Lin Yang ◽  
Athanasios A. Pantelous ◽  
Hirbod Assa
Keyword(s):  
Discrete Time ◽  
Regime Switching ◽  
Structural Changes ◽  
Linear Matrix ◽  
H Infinity Control ◽  
R Process ◽  
The Stability ◽  
Markovian Regime Switching ◽  
Markovian Regime

AbstractThe premium pricing process and the medium- and long-term stability of the reserve policy under conditions of uncertainty present very challenging issues in relation to the insurance world. Over the last two decades, applications of Markovian regime switching models to finance and macroeconomics have received strong attention from researchers, and particularly market practitioners. However, relatively little research has so far been carried out in relation to insurance. This paper attempts to consider how a linear Markovian regime switching system in discrete-time could be applied to model the medium- and long-term reserves and the premiums (abbreviated here as the P-R process) for an insurer. Some recently developed techniques from linear robust control theory are applied to explore the stability, stabilisation and robust H∞-control of a P-R system, and the potential effects of abrupt structural changes in the economic fundamentals, as well as the insurer's strategy over a finite time period. Sufficient linear matrix inequality conditions are derived for solving the proposed sub-problems. Finally, a numerical example is presented to illustrate the applicability of the theoretical results.

Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay

2014 ◽  
Vol 69 (1-2) ◽  
pp. 70-80 ◽  
Author(s):  
Mathiyalagan Kalidass ◽  
Hongye Su ◽  
Sakthivel Rathinasamy
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
The Stability ◽  
Delay Dependent

This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.

scholarly journals Stability Analysis for Discrete-Time Stochastic Fuzzy Neural Networks with Mixed Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
YaJun Li ◽  
Quanxin Zhu
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Fuzzy Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
The Novel ◽  
Free Weight ◽  
Fuzzy Neural ◽  
The Stability

This paper is concerned with the stability problem of a class of discrete-time stochastic fuzzy neural networks with mixed delays. New Lyapunov-Krasovskii functions are proposed and free weight matrices are introduced. The novel sufficient conditions for the stability of discrete-time stochastic fuzzy neural networks with mixed delays are established in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness and benefits of the proposed method.

scholarly journals The Complex Adaptive Delta-Modulator in Sliding Mode Theory

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 814
Author(s):  
Dhafer Almakhles
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Sliding Mode ◽  
Stability Conditions ◽  
Mode Theory ◽  
Dynamical Behaviors ◽  
Complex Adaptive ◽  
The Stability ◽  
Parameter Values

In this paper, we consider the stability and various dynamical behaviors of both discrete-time delta modulator (Δ-M) and adaptive Δ-M. The stability constraints and conditions of Δ-M and adaptive Δ-M are derived following the theory of quasi-sliding mode. Furthermore, the periodic behaviors are explored for both the systems with steady-state inputs and certain parameter values. The results derived in this paper are validated using simulated examples which confirms the derived stability conditions and the existence of periodicity.

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

Switching Control for a Class of Discrete-Time Switched Fuzzy Systems Based on LMI

2014 ◽  
Vol 945-949 ◽  
pp. 2543-2546
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Discrete Time ◽  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Switching Control ◽  
Linear Matrix ◽  
Common Lyapunov Function ◽  
Lyapunov Function Method ◽  
The Common ◽  
The Stability ◽  
Stability Issues

Switching control and stability issues for discrete-time switched systems whose subsystems are all discrete-time fuzzy systems are studied and new results derived. Innovated representation models for switched fuzzy systems are proposed. The common Lyapunov function method has been adopted to study the stability of this class of switched fuzzy systems. Sufficient conditions for asymptotic stability are presented. The main conditions are given in form of linear matrix inequalities (LMIs), which are easily solvable. The elaborated illustrative examples and the respective simulation experiments demonstrate the effectiveness of the proposed method.

scholarly journals Improved Delay-Dependent Stability and Stabilization Conditions of T-S Fuzzy Time-Delay Systems via an Augmented Lyapunov-Krasovskii Functional Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Zifan Gao ◽  
Jiaxiu Yang ◽  
Shuqian Zhu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stability Conditions ◽  
State Variables ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Stability And Stabilization ◽  
The Stability ◽  
Delay Dependent

This paper develops some improved stability and stabilization conditions of T-S fuzzy system with constant time-delay and interval time-varying delay with its derivative bounds available, respectively. These conditions are presented by linear matrix inequalities (LMIs) and derived by applying an augmented Lyapunov-Krasovskii functional (LKF) approach combined with a canonical Bessel-Legendre (B-L) inequality. Different from the existing LKFs, the proposed LKF involves more state variables in an augmented way resorting to the form of the B-L inequality. The B-L inequality is also applied in ensuring the positiveness of the constructed LKF and the negativeness of derivative of the LKF. By numerical examples, it is verified that the obtained stability conditions can ensure a larger upper bound of time-delay, the larger number of Legendre polynomials in the stability conditions can lead to less conservative results, and the stabilization condition is effective, respectively.

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