scholarly journals Positive Filtering withl1-Gain for Discrete-Time Positive Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Xiaoming Chen
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Positive Systems ◽  
Design Procedures ◽  
Linear Programming Problems ◽  
Error System ◽  
Necessary And Sufficient ◽  
Filtering Problem ◽  
Standard Software

This paper is concerned with the positive filtering problem for discrete-time positive systems under thel1-induced performance. We aim to propose a pair of positive filters with error-bounding features to estimate the output of positive systems. A novel characterization is first constructed so that the filtering error system is asymptotically stable with a prescribedl1-induced performance. Then, necessary and sufficient conditions for the existence of required filters are presented, and the obtained results are expressed as linear programming problems. Moreover, it is pointed out that the results can be easily checked by standard software. In addition, a numerical example is given to show the effectiveness of the proposed design procedures.

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 Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 281-288
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Error Dynamics

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.

scholarly journals H∞Control for Linear Positive Discrete-Time Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Youmei Zhang ◽  
Qingling Zhang ◽  
Tamaki Tanaka
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Positive Definite Matrix ◽  
Alternative Proof ◽  
Positive Systems ◽  
Discrete Time Systems ◽  
Separating Hyperplane ◽  
Feasible Solutions ◽  
Necessary And Sufficient ◽  
Time Systems

This paper is concerned withH∞control for linear positive discrete-time systems. Positive systems are characterized by nonnegative restriction on systems’ variables. This restriction results in some remarkable results which are available only for linear positive systems. One of them is the celebrated diagonal positive definite matrix solutions to some existed well-known results for linear systems without nonnegative restriction. We provide an alternative proof for criterion ofH∞norm by using separating hyperplane theorem and Perron-Frobenius theorem for nonnegative matrices. We also considerH∞control problem for linear positive discrete-time systems via state feedback. Necessary and sufficient conditions for such problem are presented under controller gain with and without nonnegative restriction, and then the desired controller gains can be obtained from the feasible solutions.

Stability Analysis of Switched Positive Systems with Delays

2011 ◽  
Vol 48-49 ◽  
pp. 1093-1096
Author(s):  
Xiu Yong Ding ◽  
Lan Shu ◽  
Chang Cheng Xiang ◽  
Xiu Liu
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Discrete Time ◽  
Stability Problem ◽  
Sufficient Conditions ◽  
System Stability ◽  
Positive Systems ◽  
The Stability ◽  
Switched Positive Systems ◽  
Necessary And Sufficient

This brief investigates the stability problem of discrete-time switched positive systems with delays, and establishes some necessary and sufficient conditions for the existence of a switched copositive Lyapunov function(SCLF) for such systems. It turns out that the size of the delays does not affect the stability of these systems. In other words, system stability is completely determined by the system matrices.

scholarly journals Stabilization of positive descriptor fractional discrete-time linear system with two different fractional orders by decentralized controller

2017 ◽  
Vol 65 (5) ◽  
pp. 709-714 ◽  
Author(s):  
Ł. Sajewski
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Systems ◽  
Numerical Example ◽  
Necessary And Sufficient ◽  
Fractional Orders ◽  
Time Linear

Abstract Positive descriptor fractional discrete-time linear systems with fractional different orders are addressed in the paper. The decomposition of the regular pencil is used to extend necessary and sufficient conditions for positivity of the descriptor fractional discrete-time linear system with different fractional orders. A method for finding the decentralized controller for the class of positive systems is proposed and its effectiveness is demonstrated on a numerical example.

scholarly journals Positive 2D Discrete-Time Linear Lyapunov Systems

2009 ◽  
Vol 19 (1) ◽  
pp. 95-106 ◽  
Author(s):  
Przemysław Przyborowski ◽  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Positive 2D Discrete-Time Linear Lyapunov SystemsTwo models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

Reversibility of Markov chains with applications to storage models

1985 ◽  
Vol 22 (01) ◽  
pp. 123-137 ◽  
Author(s):  
Hideo Ōsawa
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
Risk Model ◽  
Sufficient Conditions ◽  
Single Server ◽  
General State ◽  
Insurance Risk ◽  
General State Space ◽  
Necessary And Sufficient

This paper studies the reversibility conditions of stationary Markov chains (discrete-time Markov processes) with general state space. In particular, we investigate the Markov chains having atomic points in the state space. Such processes are often seen in storage models, for example waiting time in a queue, insurance risk reserve, dam content and so on. The necessary and sufficient conditions for reversibility of these processes are obtained. Further, we apply these conditions to some storage models and present some interesting results for single-server queues and a finite insurance risk model.

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