scholarly journals Linear discrete-time systems with Markovian jumps and mode dependent time-delay: Stability and stabilizability

2002 ◽  
Vol 8 (2) ◽  
pp. 123-133 ◽  
Author(s):  
E. K. Boukas ◽  
P. Shi ◽  
M. Karan ◽  
C. Y. Kaya
Keyword(s):  
Discrete Time ◽  
Stochastic Stability ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Design Algorithm ◽  
Discrete Time Systems ◽  
Stochastic Stabilizability ◽  
Time Systems ◽  
Theoretical Results

This paper considers stochastic stability and stochastic stabilizability of linear discrete-time systems with Markovian jumps and mode-dependent time-delays. Linear matrix inequality (LMI) techniques are used to obtain sufficient conditions for the stochastic stability and stochastic stabilizability of this class of systems. A control design algorithm is also provided. A numerical example is given to demonstrate the effectiveness of the obtained theoretical results.

scholarly journals Submartingales and stochastic stability

1974 ◽  
Vol 10 (2) ◽  
pp. 271-276
Author(s):  
Phil Diamond
Keyword(s):  
Lyapunov Function ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Sufficient Conditions ◽  
Discrete Time Systems ◽  
Time Systems

Sufficient conditions, involving the existence of a Lyapunov function which is a submartingale of special type, are given for the instability of stochastic discrete time systems.

scholarly journals Stability of Nonlinear Stochastic Discrete-Time Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yan Li ◽  
Weihai Zhang ◽  
Xikui Liu
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Lyapunov Functionals ◽  
Discrete Time Systems ◽  
The Stability ◽  
Efficient Criteria ◽  
Time Systems ◽  
Moment Exponential Stability ◽  
Theoretical Results

This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, andpth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.

scholarly journals Discrete-time systems with time-varying time delay: Stability and stabilizability

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
El-Kébir Boukas
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Design Algorithm ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Varying Time Delay ◽  
The Stability ◽  
Time Systems

This paper deals with the class of linear discrete-time systems with varying time delay. The problems of stability and stabilizability for this class of systems are considered. Given an upper bound and a lower bound on the time-varying delay, sufficient conditions for checking the stability of this class of systems are developed. A control design algorithm is also provided. All the results developed in this paper are in the LMI formalism which makes their solvability easier using existing tools. A numerical example is provided to show the effectiveness of the established results.

Observer-Based H∞ Feedback Control for Arbitrarily Time-Varying Discrete-Time Systems With Intermittent Measurements and Input Constraints

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Hui Zhang ◽  
Yang Shi
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time Systems ◽  
Intermittent Measurements ◽  
Time Systems ◽  
Intermittent Measurement

In this paper, we investigate the observer-based H∞ feedback control problem for discrete-time systems subject intermittent measurements and constrained control inputs. To characterize the practical scenario of the intermittent measurement phenomenon, we model it using a stochastic Bernoulli approach. We assume that the control action is constrained to be below a prescribed level. Sufficient conditions are obtained for the observer-based H∞ feedback control problem. The estimator and the controller are derived by solving a linear matrix inequality (LMI)-based optimization problem. Moreover, the proposed method is extended to systems with arbitrarily time-varying parameters within a polytope with unknown vertices. Three examples are given to illustrate the effectiveness and efficacy of the proposed method.

scholarly journals Design of Robust Output Feedback Guaranteed Cost Control for a Class of Nonlinear Discrete-Time Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yan Zhang ◽  
Yali Dong ◽  
Tianrui Li
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Cost Control ◽  
Sufficient Conditions ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Output Measurement ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems

This paper investigates static output feedback guaranteed cost control for a class of nonlinear discrete-time systems where the delay in state vector is inconsistent with the delay in nonlinear perturbations. Based on the output measurement, the controller is designed to ensure the robust exponentially stability of the closed-loop system and guarantee the performance of system to achieve an adequate level. By using the Lyapunov-Krasovskii functional method, some sufficient conditions for the existence of robust output feedback guaranteed cost controller are established in terms of linear matrix inequality. A numerical example is provided to show the effectiveness of the results obtained.

scholarly journals Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

2012 ◽  
Vol 22 (4) ◽  
pp. 451-465 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Diagram Method ◽  
State Variable ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

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