Robust Switched Filtering for Time-Varying Polytopic Uncertain Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Chang Duan ◽  
Fen Wu
Keyword(s):  
Lyapunov Function ◽  
Uncertain Systems ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Varying ◽  
Synthesis Conditions ◽  
Lmi Optimization ◽  
Globally Asymptotical Stability ◽  
Polytopic Uncertain Systems ◽  
Switching Filter

This paper studies the problem of designing robust switched filters for time-varying polytopic uncertain systems. The synthesis conditions for a set of filters under a min-switching rule are derived to guarantee globally asymptotical stability with optimized robust H∞ performance. Specifically, the conditions are expressed as bilinear matrix inequalities (BMIs) and can be solved by linear matrix inequality (LMI) optimization techniques. The proposed approach utilizes a piecewise quadratic Lyapunov function to reduce the conservativeness of robust filtering methods based on single Lyapunov function, thus better H∞ performance can be achieved. Both continuous and discrete-time robust filter designs are considered. To simplify filter implementation, a method to remove redundancy in min-switching filter members is also introduced. The advantages of the proposed robust switching filters are illustrated by several examples.

Fuzzy Control for Nonlinear Uncertain T-S Fuzzy Systems with Time-Varying Delays

2013 ◽  
Vol 341-342 ◽  
pp. 668-673
Author(s):  
Yi Min Li ◽  
Yuan Yuan Li
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Fuzzy Model ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Lmi Optimization ◽  
System A ◽  
The Stability

This paper studies the stability analysis of discrete time-varying system with parameter uncertainties and disturbances. The system under consideration is subject to time-varying non-bounded parameter uncertainties in both the state and measured output matrices. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discrete-time nonlinear system. A fuzzy observer is used to guarantee the Lyapunov stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The control and observer matrices can be obtained by directly solving a set of linear matrix inequality (LMI) via the existing LMI optimization techniques. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

Robust MPC for polytopic uncertain systems with time-varying delays

2008 ◽  
Vol 81 (8) ◽  
pp. 1239-1252 ◽  
Author(s):  
Baocang Ding ◽  
Lihua Xie ◽  
Wenjian Cai
Keyword(s):  
Uncertain Systems ◽  
Time Varying ◽  
Polytopic Uncertain Systems

New Results on Continuous-Time Switched Linear Systems With Actuator Saturation

2013 ◽  
Author(s):  
Chang Duan ◽  
Fen Wu
Keyword(s):  
Linear Systems ◽  
Differential Inclusion ◽  
Continuous Time ◽  
Actuator Saturation ◽  
Previous Method ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Switched Linear Systems ◽  
Synthesis Conditions ◽  
Lmi Optimization

This paper further studies the analysis and control problems of continuous-time switched linear systems subject to actuator saturation. Using the norm-bounded differential inclusion (NDI) description of the saturated systems and the minimal switching rule, a set of switched output feedback controllers is designed to minimize the disturbance attenuation level defined by the regional ℒ2 gain over a class of energy-bounded disturbances. The synthesis conditions are expressed as bilinear matrix inequalities (BMIs) and can be solved by numerical search coupled with linear matrix inequality (LMI) optimization. Compared to the previous method based on polytopic differential inclusion (PDI), the proposed approach has good scalability and potentially renders better performance. Numerical examples are provided to verify effectiveness of the proposed approach.

scholarly journals Novel Stability Criteria of Nonlinear Uncertain Systems with Time-Varying Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Yali Dong ◽  
Shengwei Mei ◽  
Xueli Wang
Keyword(s):  
Nonlinear Systems ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Riccati Differential Equations ◽  
Continuous State ◽  
Varying Delay

The problem of robust exponential stabilization for dynamical nonlinear systems with uncertainties and time-varying delay is considered in the paper. By constructing the proposed Lyapunov-Krasovskii functional approach, continuous state feedback controllers are put forward, and the criteria which guarantee the exponential stabilization of the nonlinear systems with uncertainties and time-varying delay are established in terms of solutions to the standard Riccati differential equations. Furthermore, based on the Lyapunov method and the linear matrix inequality approach, the sufficient conditions of exponential stability for a class of uncertain systems with time-varying delays and nonlinear perturbations are derived. Finally, two numerical examples are given to demonstrate the validity of the results.

scholarly journals Robust Exponential Stabilization for a Class of Nonlinear Uncertain Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 312-319
Author(s):  
Meng Liu ◽  
Yali Dong ◽  
Xinyue Tang
Keyword(s):  
Linear Matrix Inequality ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Robust Exponential Stabilization ◽  
Nonlinear Uncertain Systems

This paper is concerned with the problem of robust exponential stabilization for a class of nonlinear uncertain systems with time-varying delays. By using appropriately chosen Lyapunov-Krasovskii functional, together with the Finsler’s lemma, sufficient conditions for exponential stability of nonlinear uncertain systems with time-varying delays are proposed in terms of linear matrix inequality (LMI). Then, novel sufficient conditions are developed to ensure the nonlinear uncertain system with time-varying delay is robust exponentially stabilizable in terms of linear matrix inequality with state feedback control. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

Observer-based robust H∞ control for uncertain Markovian jump systems via fuzzy Lyapunov function

2018 ◽  
Vol 41 (3) ◽  
pp. 657-667 ◽  
Author(s):  
Jun Chen ◽  
Tieqing He ◽  
Fei Liu
Keyword(s):  
Lyapunov Function ◽  
External Disturbance ◽  
Optimization Techniques ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Congruent Transformation ◽  
Fuzzy Lyapunov Function ◽  
Jump Systems ◽  
Takagi Sugeno

This paper investigates the problem of observer-based robust [Formula: see text] control for a class of continuous-time nonlinear Markovian jump systems (MJSs) with uncertainties, external disturbance and unavailable states that can be represented by Takagi-Sugeno (T-S) fuzzy models. Based on a mode-dependent fuzzy Lyapunov function and by introducing slack matrix variables, a sufficient condition for the existence of the state observer and observer-based robust [Formula: see text] controller for such MJSs are derived by constructing an augmented fuzzy system. Further, by means of congruent transformation in matrix and linear matrix inequality (LMI) method, the results are given in the form of LMIs that can be easily solved by using the convex optimization techniques. Moreover, we also give the result obtained via common stochastic Lyapunov function to compare with the proposed approach. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

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