Robust Kalman Filtering for Discrete-Time Time-Varying Systems With Stochastic and Norm-Bounded Uncertainties

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Mahdi Abolhasani ◽  
Mehdi Rahmani
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Optimization Problem ◽  
Stochastic Systems ◽  
Estimation Error ◽  
Linear Matrix ◽  
Time Varying ◽  
Unknown Parameters ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

In this paper, a new robust Kalman filter is proposed for discrete-time time-varying linear stochastic systems. The system under consideration is subject to stochastic and norm-bounded uncertainties in all matrices of the system model. In the proposed approach, the filter is first achieved by solving a stochastic min–max optimization problem. Next, we find an upper bound on the estimation error covariance, and then, by using a linear matrix inequality (LMI) optimization problem, unknown parameters of the filter are determined such that the obtained upper bound is minimized. Finally, two numerical examples are given to demonstrate the effectiveness and performance of the proposed filtering approach compared to the existing robust filters.

scholarly journals Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Feten Gannouni ◽  
Fayçal Ben Hmida
Keyword(s):  
Convex Optimization ◽  
State Estimation ◽  
Discrete Time ◽  
Upper Bound ◽  
Optimization Problem ◽  
Estimation Error ◽  
Original System ◽  
Error Variance ◽  
Linear Matrix ◽  
Convex Optimization Problem

We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF) having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI) for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation.

Improved Delay-Dependent Robust Stability Criteria for Discrete-Time Stochastic Uncertain Networks with Time-Varying Delays

2012 ◽  
Vol 430-432 ◽  
pp. 849-852
Author(s):  
Meng Zhuo Luo ◽  
Shou Ming Zhong
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Time Varying ◽  
Mean Square ◽  
Stability Criteria ◽  
The Mean ◽  
Delay Dependent ◽  
Uncertain Networks ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

In this paper, the mean square asymptotical stability is investigated for a class of discrete-time stochastic systems with time-varying delays and norm-bounded uncertainties,a numerical example is presented to show the usefulness of the derived LMI-based stability condition.

Observer-Based Stabilization of Linear Discrete Time-Varying Delay Systems

2021 ◽  
Author(s):  
Venkatesh Modala ◽  
Sourav Patra ◽  
Goshaidas Ray
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stabilizing Controller ◽  
Time Varying Delay ◽  
Convex Inequality ◽  
Summation Inequality ◽  
Delay Dependent

Abstract This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov-Krasovskii (LK) functional to derive a delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus, ensure global asymptotic stability in presence of any time delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.

Delay-Dependent Robust Control for Discrete-Time Uncertain Stochastic Systems With Time-Varying Delays

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Guan-Wei Chen
Keyword(s):  
Robust Control ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Gain Scheduled Controller ◽  
Delay Dependent

This paper investigates a delay-dependent robust control problem of discrete-time uncertain stochastic systems with delays. The uncertainty considered in this paper is time-varying but norm-bounded, and the delays are considered as interval time-varying case for both state and input. According to the considerations of uncertainty, stochastic behavior, and time delays, the problem considered in this paper is more general than the existing works for uncertain stochastic systems. Via the proposed Lyapunov–Krasovskii function, some sufficient conditions are derived into the extended linear matrix inequality form. Moreover, Jensen inequality and free matrix equation are employed to reduce conservatism of those conditions. Through using the proposed design method, a gain-scheduled controller is designed to guarantee asymptotical stability of uncertain stochastic systems in the sense of mean square. Finally, two numerical examples are provided to demonstrate applicability and effectiveness of the proposed design method.

scholarly journals Analysis of Discrete-Time H2 Guaranteed Cost Performance

2009 ◽  
Author(s):  
Richard Conway ◽  
Roberto Horowitz
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Optimization Problem ◽  
Parametric Uncertainty ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Cost Performance ◽  
Lti System ◽  
Dynamic Uncertainty ◽  
Guaranteed Cost

This paper presents a methodology for analyzing the H2 guaranteed cost performance of a discrete-time LTI system with unstructured dynamic uncertainty. Using the methods of guaranteed cost control, an upper bound on H2 guaranteed cost performance over unstructured parametric uncertainty is formulated in terms of feasibility of a linear matrix inequality. It is then shown that the feasibility of this inequality also guarantees the same level of performance also over unstructured dynamic uncertainty. This is then used to formulate the problem of finding the best upper bound on H2 guaranteed cost performance over unstructured causal dynamic uncertainty as a semi-definite program. Finally, it is shown that this optimization problem can be solved efficiently and accurately using discrete algebraic Riccati equations.

scholarly journals LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

2012 ◽  
Vol 22 (2) ◽  
pp. 339-351 ◽  
Author(s):  
Pagavathigounder Balasubramaniam ◽  
Shanmugam Lakshmanan ◽  
Rajan Rakkiyappan
Keyword(s):  
Robust Stability ◽  
Optimization Problem ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Lmi Optimization ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertaintiesThis paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.

scholarly journals Robust Stability and Stabilization of a Class of Uncertain Nonlinear Discrete-Time Stochastic Systems with Interval Time-Varying Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shuang Liang ◽  
Yali Dong
Keyword(s):  
Discrete Time ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Stochastic Stabilization ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper deals with the problems of the robust stochastic stability and stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays and nonlinear disturbances. By utilizing a new Lyapunov-Krasovskii functional and some well-known inequalities, some new delay-dependent criteria are developed to guarantee the robust stochastic stability of a class of uncertain discrete-time stochastic systems in terms of the linear matrix inequality (LMI). Then based on the state feedback controller, the delay-dependent sufficient conditions of robust stochastic stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays are established. The controller gain is designed to ensure the robust stochastic stability of the closed-loop system. Finally, illustrative examples are given to demonstrate the effectiveness of the proposed method.

scholarly journals RobustH∞Filtering for Uncertain Discrete-Time Fuzzy Stochastic Systems with Sensor Nonlinearities and Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Mingang Hua ◽  
Pei Cheng ◽  
Juntao Fei ◽  
Jianyong Zhang ◽  
Junfeng Chen
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Error System ◽  
Varying Delay

The robust filtering problem for a class of uncertain discrete-time fuzzy stochastic systems with sensor nonlinearities and time-varying delay is investigated. The parameter uncertainties are assumed to be time varying norm bounded in both the state and measurement equations. By using the Lyapunov stability theory and some new relaxed techniques, sufficient conditions are proposed to guarantee the robustly stochastic stability with a prescribedH∞performance level of the filtering error system for all admissible uncertainties, sensor nonlinearities, and time-varying delays. These conditions are dependent on the lower and upper bounds of the time-varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods.

scholarly journals Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Yanfeng Zhao ◽  
Jihong Shen ◽  
Dongyan Chen
Keyword(s):  
Discrete Time ◽  
Regulatory Networks ◽  
Estimation Error ◽  
Estimation Method ◽  
Genetic Regulatory Networks ◽  
Independent Random Variables ◽  
Linear Matrix ◽  
Time Varying ◽  
State Estimator ◽  
Randomly Occurring Uncertainties

We deal with the design problem of nonfragile state estimator for discrete-time genetic regulatory networks (GRNs) with time-varying delays and randomly occurring uncertainties. In particular, the norm-bounded uncertainties enter into the GRNs in random ways in order to reflect the characteristic of the modelling errors, and the so-called randomly occurring uncertainties are characterized by certain mutually independent random variables obeying the Bernoulli distribution. The focus of the paper is on developing a new nonfragile state estimation method to estimate the concentrations of the mRNA and the protein for considered uncertain delayed GRNs, where the randomly occurring estimator gain perturbations are allowed. By constructing a Lyapunov-Krasovskii functional, a delay-dependent criterion is obtained in terms of linear matrix inequalities (LMIs) by properly using the discrete-time Wirtinger-based inequality and reciprocally convex combination approach as well as the free-weighting matrix method. It is shown that the proposed method ensures that the estimation error dynamics is globally asymptotically stable and the desired estimator parameter is designed via the solutions to certain LMIs. Finally, we provide two numerical examples to illustrate the feasibility and validity of the proposed estimation results.

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