Model-Based Discrete Linear State Estimator for Nonlinearizable Systems With State-Dependent Noise

1990 ◽  
Vol 112 (4) ◽  
pp. 774-781 ◽  
Author(s):  
R. J. Chang
Keyword(s):  
Discrete Time ◽  
Continuous Model ◽  
Equivalent Model ◽  
State Estimator ◽  
Time Model ◽  
State Dependent ◽  
Present Technique ◽  
Linear State ◽  
Noisy Measurement ◽  
Time Linear

A practical technique to derive a discrete-time linear state estimator for estimating the states of a nonlinearizable stochastic system involving both state-dependent and external noises through a linear noisy measurement system is presented. The present technique for synthesizing a discrete-time linear state estimator is first to construct an equivalent reference linear model for the nonlinearizable system such that the equivalent model will provide the same stationary covariance response as that of the nonlinear system. From the linear continuous model, a discrete-time state estimator can be directly derived from the corresponding discrete-time model. The synthesizing technique and filtering performance are illustrated and simulated by selecting linear, linearizable, and nonlinearizable systems with state-dependent noise.

scholarly journals Optimal guaranteed cost filtering for Markovian jump discrete-time systems

2004 ◽  
Vol 2004 (1) ◽  
pp. 33-48 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Peng Shi
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Estimation Error ◽  
Linear Matrix ◽  
State Estimator ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Discrete Time Systems ◽  
Linear State ◽  
Time Systems

This paper develops a result on the design of robust steady-state estimator for a class of uncertain discrete-time systems with Markovian jump parameters. This result extends the steady-state Kalman filter to the case of norm-bounded time-varying uncertainties in the state and measurement equations as well as jumping parameters. We derive a linear state estimator such that the estimation-error covariance is guaranteed to lie within a certain bound for all admissible uncertainties. The solution is given in terms of a family of linear matrix inequalities (LMIs). A numerical example is included to illustrate the theory.

New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems

2019 ◽  
Vol 20 (3-4) ◽  
pp. 315-323
Author(s):  
Hongli Yang ◽  
Yuexiao Jia
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
The State ◽  
Practical Stability ◽  
Space Systems ◽  
State Matrix ◽  
Numerical Examples ◽  
State Space Systems ◽  
Linear State ◽  
Time Linear

AbstractPractical stability of a fractional order discrete-time linear state-space systems was put up in recent years. It is usually checked by the eigenvalues of the state matrix, some methods have been given during these years. But if the size of the state matrix is large, the computations of eigenvalues can be very onerous. In this paper, some new conditions on practical stability for positive fractional discrete-time linear system are presented. Numerically checking method of practical stability is presented based on the new conditions given in this paper. It is illustrated by the numerical examples that our checking method is effective and true. Compared to the now existing methods, numerically checking method is an attractive method because it’s easily implemented.

Set-Membership Filtering-Based Leader–Follower Synchronization of Discrete-Time Linear Multi-Agent Systems

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Diganta Bhattacharjee ◽  
Kamesh Subbarao
Keyword(s):  
Discrete Time ◽  
The State ◽  
Multi Agent Systems ◽  
State Estimator ◽  
Agent Systems ◽  
Set Membership ◽  
Multi Agent ◽  
Bounded Input ◽  
Time Linear ◽  
Synchronization Protocol

Abstract In this paper, a set-membership filtering-based leader–follower synchronization protocol for discrete-time linear multi-agent systems is proposed, wherein the aim is to make the agents synchronize with a leader. The agents, governed by identical high-order discrete-time linear dynamics, are subject to unknown-but-bounded input disturbances. In terms of its own state information, each agent only has access to measured outputs that are corrupted with unknown-but-bounded output disturbances. Also, the initial states of the agents are unknown. To deal with all these unknowns (or uncertainties), a set-membership filter (or state estimator), having the “correction-prediction” form of a standard Kalman filter, is formulated. We consider each agent to be equipped with this filter that estimates the state of the agent and consider the agents to be able to share the state estimate information with the neighbors locally. The corrected state estimates of the agents are utilized in the local control law design for synchronization. Under appropriate conditions, the global disagreement error between the agents and the leader is shown to be bounded. An upper bound on the norm of the global disagreement error is calculated and shown to be monotonically decreasing. Finally, a simulation example is included to illustrate the effectiveness of the proposed leader–follower synchronization protocol.

scholarly journals Stoichiometric knife-edge model on discrete time scale

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ming Chen ◽  
Lale Asik ◽  
Angela Peace
Keyword(s):  
Discrete Time ◽  
Time Scale ◽  
Ecological Stoichiometry ◽  
Discrete Model ◽  
Nutrient Content ◽  
Continuous Model ◽  
Knife Edge ◽  
Time Model ◽  
Predator Prey ◽  
Predator Prey Model

AbstractEcological stoichiometry is the study of the balance of multiple elements in ecological interactions and processes (Sterner and Elser in Ecological Stoichiometry: The Biology of Elements from Molecules to the Biosphere, 2002). Modeling under this framework enables us to investigate the effect nutrient content on organisms whether the imbalance involves insufficient or excess nutrient content. This phenomenon is called the “stoichiometric knife-edge”. In this paper, a discrete-time predator–prey model that captures this phenomenon is established and qualitatively analyzed. We systematically expound the similarities and differences between our discrete model and the corresponding continuous analog. Theoretical and numerical analyses show that while the discrete and continuous models share many properties, differences also exist. Under certain parameter sets, the models exhibit qualitatively different dynamics. While the continuous model shows limit cycle, Hopf bifurcation, and saddle-node bifurcation, the discrete-time model exhibits richer dynamical behaviors, such as chaos. By comparing the dynamics of the continuous and discrete model, we can conclude that stoichiometric effects of low food quality on predators are robust to the discretization of time. This study can possibly serve as an example for pointing to the importance of time scale in ecological modeling.

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