scholarly journals Controllability Analysis of Linear Discrete Time Systems with Time Delay in State

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Wenguang Luo
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Delay ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

The controllability issues for linear discrete-time systems with delay in state are addressed. By introducing a new concept, the minimum controllability realization index (MinCRI), the characteristic of controllability is revealed. It is proved that the MinCRI of a system with state delay exists and is finite. Based on this result, a necessary and sufficient condition for the controllability of discrete-time linear systems with state delay is established.

scholarly journals Controllability of Linear Discrete-Time Systems with Both Delayed States and Delayed Inputs

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Wenguang Luo
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Control Delay ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
And Control ◽  
Time Systems ◽  
Time Linear

The controllability issues for discrete-time linear systems with delay in state and control are addressed. By introducing a new concept, the controllability realization index (CRI), the characteristic of controllability is revealed. An easily testable necessary and sufficient condition for the controllability of discrete-time linear systems with state and control delay is established.

scholarly journals Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear Systems

2009 ◽  
Vol 19 (2) ◽  
pp. 263-269 ◽  
Author(s):  
Mikołaj Busłowicz ◽  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Practical Implementation ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear SystemsIn the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical examples.

scholarly journals Losslessness of Nonlinear Stochastic Discrete-Time Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Xikui Liu ◽  
Yan Li ◽  
Ning Gao
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Zero Dynamics ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree0,…,0and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.

scholarly journals H-Index for Stochastic Linear Discrete-Time Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Yan Li ◽  
Weihai Zhang ◽  
Xikui Liu
Keyword(s):  
Discrete Time ◽  
Observer Design ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
H Index ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Index Problem ◽  
Time Systems ◽  
Theoretical Results

This paper discusses theH-index problem for stochastic linear discrete-time systems. A necessary and sufficient condition ofH-index is given for such systems in finite horizon. It is proved that when theH-index is greater than a given value, the feasibility ofH-index is equivalent to the solvability of a constrained difference equation. The above result can be applied to the fault detection observer design. Finally, some examples are presented to illustrate the proposed theoretical results.

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.

scholarly journals Finite-Time Stability Analysis of Discrete-Time Linear Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Songlin Wo ◽  
Xiaoxin Han
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Singular Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Time Stability ◽  
Finite Time Stability ◽  
Necessary And Sufficient ◽  
Time Linear

The finite-time stability (FTS) problem of discrete-time linear singular systems (DTLSS) is considered in this paper. A necessary and sufficient condition for FTS is obtained, which can be expressed in terms of matrix inequalities. Then, another form of the necessary and sufficient condition for FTS is also given by using matrix-null space technology. In order to solve the stability problem expediently, a sufficient condition for FTS is given via linear matrix inequality (LMI) approach; this condition can be expressed in terms of LMIs. Finally, an illustrating example is also given to show the effectiveness of the proposed method.

Robust stability of positive discrete-time linear systems of fractional order

2010 ◽  
Vol 58 (4) ◽  
pp. 567-572 ◽  
Author(s):  
M. Busłowicz
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Robust Stability ◽  
Discrete Time ◽  
Natural Order ◽  
Discrete Time System ◽  
Uncertainty Structure ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Robust stability of positive discrete-time linear systems of fractional orderThe paper is devoted to the problem of robust stability of linear positive discrete-time systems of fractional order with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of linear uncertainty structure with unity rank uncertainty structure and with non-negative perturbation matrices, are established. It is shown that robust stability of the positive discrete-time fractional system is equivalent to: 1) robust stability of the corresponding positive discrete-time system of natural order - in the general case, 2) robust stability of the corresponding finite family of positive discrete-time systems of natural order - in the case of linear unity rank uncertainty structure, 3) asymptotic stability of only one corresponding positive discrete-time system of natural order - in the case of linear uncertainty structure with non-negative perturbation matrices. Moreover, simple necessary and sufficient condition for robust stability of the positive interval discrete-time linear systems of fractional order is given. The considerations are illustrated by numerical examples.

Sign in / Sign up

Export Citation Format

Share Document