Stability analysis of nonlinear impulsive switched positive systems

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Yanzi Lin ◽  
Ping Zhao
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Function Method ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Positive Systems ◽  
Lyapunov Function Method ◽  
The Stability ◽  
Switched Positive Systems ◽  
Time Linear

Abstract In this paper, the global asymptotic stability (GAS) of continuous-time and discrete-time nonlinear impulsive switched positive systems (NISPS) are studied. For continuous-time and discrete-time NISPS, switching signals and impulse signals coexist. For both of these systems, using the multiple max-separable Lyapunov function method and average dwell-time (ADT) method, some sufficient conditions on GAS are given. Based on these, the GAS criteria are also given for continuous-time and discrete-time linear impulsive switched positive systems (LISPS). From our criteria, the stability of the systems can be judged directly from the characteristics of the system functions, switching signals and impulse signals of the systems. Finally, simulation examples verify the validity of the results.

Stability Analysis of Switched Positive Systems with Delays

2011 ◽  
Vol 48-49 ◽  
pp. 1093-1096
Author(s):  
Xiu Yong Ding ◽  
Lan Shu ◽  
Chang Cheng Xiang ◽  
Xiu Liu
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Discrete Time ◽  
Stability Problem ◽  
Sufficient Conditions ◽  
System Stability ◽  
Positive Systems ◽  
The Stability ◽  
Switched Positive Systems ◽  
Necessary And Sufficient

This brief investigates the stability problem of discrete-time switched positive systems with delays, and establishes some necessary and sufficient conditions for the existence of a switched copositive Lyapunov function(SCLF) for such systems. It turns out that the size of the delays does not affect the stability of these systems. In other words, system stability is completely determined by the system matrices.

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 Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model

2016 ◽  
Vol 26 (4) ◽  
pp. 441-452 ◽  
Author(s):  
Andrzej Ruszewski
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Numerical Examples ◽  
New Model ◽  
The Stability ◽  
Partition Method ◽  
Necessary And Sufficient ◽  
Time Linear ◽  
Linear Scalar

Abstract The stability problems of fractional discrete-time linear scalar systems described by the new model are considered. Using the classical D-partition method, the necessary and sufficient conditions for practical stability and asymptotic stability are given. The considerations are il-lustrated by numerical examples.

New stabilization results for discrete-time positive switched systems with forward mode-dependent average dwell time

2016 ◽  
Vol 39 (2) ◽  
pp. 224-229 ◽  
Author(s):  
Tingting Liu ◽  
Baowei Wu ◽  
Yue-E Wang ◽  
Lili Liu
Keyword(s):  
Discrete Time ◽  
Switched Systems ◽  
Dwell Time ◽  
Stability Result ◽  
Average Dwell Time ◽  
Feedback Controllers ◽  
Multiple Sample ◽  
The Stability ◽  
Positive Switched Systems ◽  
Time Linear

The stability and stabilization of discrete-time linear positive switched systems are discussed in this paper. First, based on the concept of the forward mode-dependent average dwell time, a stability result for discrete-time linear positive switched systems is obtained by utilizing the multiple linear copositive Lyapunov functions. Then, by introducing multiple-sample Lyapunov-like functions variation, a new exponential stability result is derived. Finally, the conditions for the existence of mode-dependent stabilizing state feedback controllers are investigated, and two illustrative examples are given to show the correctness of the theoretical results obtained.

scholarly journals Checking of the positivity of descriptor linear systems with singular pencils

2012 ◽  
Vol 22 (1) ◽  
pp. 77-86 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
Necessary And Sufficient ◽  
Descriptor Linear Systems ◽  
Time Linear

Checking of the positivity of descriptor linear systems with singular pencilsA method for checking of the positivity of descriptor continuous-time and discrete-time linear systems with singular pencil is proposed. The method is based on elementary row and column operations on the matrices of descriptor systems. Necessary and sufficient conditions for the positivity of the descriptor systems are established.

scholarly journals Fractional Positive Continuous-Time Linear Systems and Their Reachability

2008 ◽  
Vol 18 (2) ◽  
pp. 223-228 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Positive Systems ◽  
State Equations ◽  
Fractional Systems ◽  
New Class ◽  
The Laplace Transform ◽  
Necessary And Sufficient ◽  
Time Linear

Fractional Positive Continuous-Time Linear Systems and Their ReachabilityA new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.

scholarly journals Stabilization of a Class of Continuous-Time Switched Systems with State Constraints via a Mode-Dependent Switching Method

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Qingyu Su ◽  
Peipei Wang
Keyword(s):  
Continuous Time ◽  
Switched Systems ◽  
Dwell Time ◽  
State Constraints ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Decay Rates ◽  
Average Dwell Time Method ◽  
The Stability ◽  
Switching Method

The stability and the stabilization problems for a class of continuous-time switched systems with state constraints via a mode-dependent switching method are investigated. The paper presents an improved average dwell time method, which considers different decay rates of a Lyapunov function related to each of the active subsystems according to whether the saturations occur or not, respectively. It is shown that the improved average dwell time method is less conservative than the common average dwell time method. Based on the improved average dwell time method, the sufficient conditions and state feedback controllers for stabilization of the switched system are derived. A numerical example is given to illustrate the proposed approach.

scholarly journals Stabilization of positive descriptor fractional discrete-time linear system with two different fractional orders by decentralized controller

2017 ◽  
Vol 65 (5) ◽  
pp. 709-714 ◽  
Author(s):  
Ł. Sajewski
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Systems ◽  
Numerical Example ◽  
Necessary And Sufficient ◽  
Fractional Orders ◽  
Time Linear

Abstract Positive descriptor fractional discrete-time linear systems with fractional different orders are addressed in the paper. The decomposition of the regular pencil is used to extend necessary and sufficient conditions for positivity of the descriptor fractional discrete-time linear system with different fractional orders. A method for finding the decentralized controller for the class of positive systems is proposed and its effectiveness is demonstrated on a numerical example.

Positivity and Stability of Standard and Fractional Descriptor Continuous-Time Linear and Nonlinear Systems

2018 ◽  
Vol 19 (3-4) ◽  
pp. 299-307 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Linear And Nonlinear Systems ◽  
Time Linear

AbstractThe positivity and stability of standard and fractional descriptor continuous-time linear and nonlinear systems are addressed. Necessary and sufficient conditions for the positivity of descriptor linear and sufficient conditions for nonlinear systems are established. Using an extension of Lyapunov method sufficient conditions for the stability of positive nonlinear systems are given. The considerations are extended to fractional nonlinear systems.

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