scholarly journals Stabilization of nonlinear discrete-time systems via a digital communication channel

2005 ◽  
Vol 2005 (1) ◽  
pp. 43-56 ◽  
Author(s):  
V. N. Phat ◽  
J. Jiang
Keyword(s):  
Discrete Time ◽  
Communication Channel ◽  
Digital Communication ◽  
Sufficient Conditions ◽  
Constructive Method ◽  
Control Input ◽  
Stabilizing Controller ◽  
Discrete Time Systems ◽  
Global And Local ◽  
Time Systems

We deal with the stabilization problem for a class of nonlinear discrete-time systems via a digital communication channel. We consider the case when the control input is to be transmitted via communication channels with a bit-rate constraint. Under an appropriate growth condition on the nonlinear perturbation, we establish sufficient conditions for the global and local stabilizability of semilinear and nonlinear discrete-time systems, respectively. A constructive method to design a feedback stabilizing controller is proposed.

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 Positive Partial Realization Problem for Linear Discrete-Time Systems

2007 ◽  
Vol 17 (2) ◽  
pp. 165-171 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Impulse Response ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Finite Sequence ◽  
Realization Problem ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Time Systems

Positive Partial Realization Problem for Linear Discrete-Time SystemsA partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.

scholarly journals Iterative Learning Control for Linear Discrete-Time Systems with Randomly Variable Input Trail Length

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Yun-Shan Wei ◽  
Qing-Yuan Xu
Keyword(s):  
Discrete Time ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Control Input ◽  
Initial State ◽  
Tracking Errors ◽  
Discrete Time Systems ◽  
P Type ◽  
Time Systems

For linear discrete-time systems with randomly variable input trail length, a proportional- (P-) type iterative learning control (ILC) law is proposed. To tackle the randomly variable input trail length, a modified control input at the desirable trail length is introduced in the proposed ILC law. Under the assumption that the initial state fluctuates around the desired initial state with zero mean, the designed ILC scheme can drive the ILC tracking errors to zero at the desirable trail length in expectation sense. The designed ILC algorithm allows the trail length of control input which is different from system state and output at a specific iteration. In addition, the identical initial condition widely used in conventional ILC design is also mitigated. An example manifests the validity of the proposed ILC algorithm.

AN OPTIMIZATION APPROACH TO THE DESIGN OF CONSTRAINED REGULATORS FOR UNCERTAIN DISCRETE-TIME SYSTEMS

2006 ◽  
Vol 15 (03) ◽  
pp. 373-387
Author(s):  
M. VASSILAKI ◽  
G. BITSORIS
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Optimization Approach ◽  
Control Constraints ◽  
Existence Of A Solution ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
And Control ◽  
Time Systems ◽  
State And Control Constraints

In this paper the regulation problem of linear discrete-time systems with uncertain parameters under state and control constraints is studied. In the first part of the paper, two theorems concerning necessary and sufficient conditions for the existence of a solution to this problem are presented. Due to the constructive form of the proof of these theorems, these results can be used to the development of techniques for the derivation of a control law transferring to the origin any state belonging to a given set of initial states while respecting the state and control constraints.

Sliding Mode Control of Discrete-Time Systems

2000 ◽  
Vol 122 (4) ◽  
pp. 793-802 ◽  
Author(s):  
A. Jafari Koshkouei ◽  
A. S. I. Zinober
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Control Design ◽  
Continuous Case ◽  
Mode Control ◽  
Discrete Time Systems ◽  
Set Of Points ◽  
Time Systems

In discrete-time systems, instead of having a hyperplane as in the continuous case, there is a countable set of points comprising a so-called lattice; and the surface on which these sliding points lie is the latticewise hyperplane. In this paper the concept of multivariable discrete-time sliding mode is clarified and new sufficient conditions for the existence of the sliding mode are presented. A new control design using the properties of discrete sliding is proposed, and the behavior of the system in the sliding mode is studied. Furthermore, the stabilization of discrete-time systems and an optimal sliding lattice are considered. [S0022-0434(00)02804-5]

scholarly journals Absolute stability of a class of fractional positive nonlinear systems

2019 ◽  
Vol 29 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Time Systems ◽  
The Absolute ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.

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