scholarly journals Interval criterion for stability analysis of discrete-time nonlinear systems with partial state saturation nonlinearities

2006 ◽  
Vol 19 (2) ◽  
pp. 271-286
Author(s):  
Lubomir Kolev ◽  
Simona Filipova-Petrakieva ◽  
Valeri Mladenov
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Interval Uncertainties ◽  
Partial State ◽  
Definite Interval ◽  
Outer Bounds ◽  
State Saturation

A generalization of sufficient conditions for global asymptotic stability of the equilibrium of discrete-time nonlinear systems with saturation non linearity's on part of the states in the case of interval uncertainties is considered. When using quadratic form Lyapunov functions, sufficient conditions based on the positive definite interval matrices are presented. In order to check this, a recently proposed method for determining the outer bounds of eigenvalues ranges is used. A numerical example illustrating the applicability of the method suggested is solved in the end of the paper.

Uniform Stability of Discrete-Time Switched Nonlinear Systems

2014 ◽  
Vol 643 ◽  
pp. 83-89
Author(s):  
Shu Rong Sun ◽  
Guang Rong Zhang ◽  
Ping Zhao
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Uniform Stability ◽  
Switched Nonlinear Systems ◽  
Uniform Asymptotic Stability ◽  
Unstable Subsystems ◽  
The Stability

In this paper, we study the stability properties of a general class of nonautonomous discrete-time switched nonlinear systems. The switched systems consist of stable and unstable subsystems. Based on Lyapunov functions, some sufficient conditions for uniform stability, uniform asymptotic stability and uniform exponential stability are established.

scholarly journals Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 281-288
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Error Dynamics

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.

scholarly journals Absolute stability of a class of fractional positive nonlinear systems

2019 ◽  
Vol 29 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Time Systems ◽  
The Absolute ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.

scholarly journals Global Stability of Positive Discrete-time Time-varying Nonlinear Feedback Systems

2021 ◽  
Vol 3 (1) ◽  
pp. 17-20
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Global Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Positive Time

The global stability of positive  discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.

New Analysis/Design of Generalized Discrete PI Controller via Discrete Time Delay Control for Nonlinear Systems

2020 ◽  
Author(s):  
Suresh B. Reddy
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Pi Controller ◽  
Pid Controllers ◽  
Analysis And Design ◽  
Proportional Integral ◽  
Discrete Time Delay

Abstract Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) controllers are among the most common schemes for control since their formulation nearly a century ago. They have been very successful in many applications, even as we have migrated from analog implementations to digital control systems. While there is rich literature for design and analysis of PI/PID controllers for linear time-invariant systems with modeled dynamics, the tools for analysis and design for nonlinear systems with unknown dynamics are limited, despite their known effectiveness. This paper extends previous observations about a form of discrete Time Delay Control’s equivalence to a generalized PI controller for more general canonical systems, with additional complimentary feedback linearization of known dynamics, as desired. In addition, sufficient conditions for Bounded Input-Bounded Output (BIBO) as well as exponential stability are developed in this paper for the form of discrete TDC that is closest to generalized discrete PI equivalent controller, for multi-input multi-output nonlinear systems, including nonaffine cases. Accordingly, design procedures are suggested for such discrete TDC, and generalized discrete PI controller for nonlinear systems.

scholarly journals Fractional descriptor standard and positive discrete-time nonlinear systems

2015 ◽  
Vol 63 (3) ◽  
pp. 651-655
Author(s):  
T. Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Example ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

AbstractA method of analysis of the fractional descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on a numerical example.

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