Periodically time-varying controller synthesis for multiobjective control of discrete-time systems and analysis of achievable performance

2011 ◽  
Vol 60 (9) ◽  
pp. 709-717 ◽  
Author(s):  
Yoshio Ebihara ◽  
Jun Yamaguchi ◽  
Tomomichi Hagiwara
Keyword(s):  
Discrete Time ◽  
Controller Synthesis ◽  
Time Varying ◽  
Multiobjective Control ◽  
Discrete Time Systems ◽  
Time Systems

scholarly journals Reachable Set Estimation for Discrete-Time Systems with Interval Time-Varying Delays and Bounded Disturbances

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Jiemei Zhao ◽  
Yin Sheng
Keyword(s):  
Discrete Time ◽  
Reachable Set ◽  
Time Varying ◽  
Time Varying Delay ◽  
Set Estimation ◽  
Discrete Time Systems ◽  
Bounded Disturbances ◽  
Reachable Set Estimation ◽  
Time Systems ◽  
Varying Delay

The reachable set estimation problem for discrete-time systems with delay-range-dependent and bounded disturbances is investigated. A triple-summation term, the upper bound, and the lower bound of time-varying delay are introduced into the Lyapunov function. In this case, an improved delay-range-dependent criterion is established for the addressed problem by constructing the appropriate Lyapunov functional, which guarantees that the reachable set of discrete-time systems with time-varying delay and bounded peak inputs is contained in the ellipsoid. It is worth mentioning that the initial value of the system does not need to be zero. Then, the reachable set estimation problem for time-delay systems with polytopic uncertainties is investigated. The effectiveness and the reduced conservatism of the derived results are demonstrated by an illustrative example.

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>

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