scholarly journals Simple stability conditions of linear discrete time systems with multiple delay

2010 ◽  
Vol 7 (1) ◽  
pp. 69-79 ◽  
Author(s):  
Sreten Stojanovic ◽  
Dragutin Debeljkovic
Keyword(s):  
Discrete Time ◽  
Stability Conditions ◽  
Multiple Delay ◽  
Discrete Time Systems ◽  
Time Systems

scholarly journals New stability conditions for a class of nonlinear discrete-time systems with time-varying delay

2021 ◽  
Author(s):  
SAMI ELMADSSIA ◽  
KARIM SADAAOUI
Keyword(s):  
Discrete Time ◽  
Stability Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Matrix Properties ◽  
Arrow Form Matrix ◽  
Bounded Nonlinearity ◽  
Time Systems ◽  
Varying Delay

The problem of stability analysis for a class of nonlinear discrete time systems with time varying delay is studied in this work. Such systems are modeled by delayed difference equations. Subsequently, this system is transformed into an arrow form matrix representation. Using M-matrix properties, novel sufficient stability conditions are determined. It is shown how to use our method to design a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of a nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Several examples are provided to show the effectiveness of the introduced technique. <br>

scholarly journals New stability conditions for class of nonlinear discrete-time systems with time-varying delay

2021 ◽  
Author(s):  
SAMI ELMADSSIA ◽  
KARIM SADAAOUI
Keyword(s):  
Discrete Time ◽  
Stability Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Matrix Properties ◽  
Arrow Form Matrix ◽  
Bounded Nonlinearity ◽  
Time Systems ◽  
Varying Delay

The problem of stability analysis for a class of nonlinear discrete time systems with time varying delay is studied in this work. Such systems are modeled by delayed difference equations. Subsequently, this system is transformed into an arrow form matrix representation. Using M-matrix properties, novel sufficient stability conditions are determined. It is shown how to use our method to design a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of a nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Several examples are provided to show the effectiveness of the introduced technique. <br>

scholarly journals New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1531 ◽  
Author(s):  
Sami Elmadssia ◽  
Karim Saadaoui
Keyword(s):  
Discrete Time ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Aggregation Techniques ◽  
Discrete Time Delay ◽  
Time Systems ◽  
Varying Delay

In this paper, the stability problem of discrete time delay systems is investigated. The class of systems under consideration is represented by delayed difference equations and models nonlinear discrete time systems with time varying delay. It is transformed into an arrow from matrix representation which allows the use of aggregation techniques and M-matrix properties to determine novel sufficient stability conditions. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Next, it is shown how to use our method in designing a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. Finally, several examples are provided to show the effectiveness of the introduced technique.

Sign in / Sign up

Export Citation Format

Share Document