Observer-based robust exponential stabilization for linear systems with parameter uncertainties

2020 ◽  
Author(s):  
Xuesheng Zhang ◽  
Jian Hu ◽  
Lin Long ◽  
Wei Zhang
Keyword(s):  
Linear Systems ◽  
Exponential Stabilization ◽  
Parameter Uncertainties ◽  
Robust Exponential Stabilization

scholarly journals ℋ∞Performance and Stability Analysis of Linear Systems with Interval Time-Varying Delays and Stochastic Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Stochastic Parameter ◽  
Stochastic Properties ◽  
Random Change

This paper deals with the problems ofℋ∞performance and stability analysis for linear systems with interval time-varying delays. It is assumed that the parameter uncertainties are of stochastic properties to represent random change of various environments. By constructing a newly augmented Lyapunov-Krasovskii functional, less conservative criteria of the concerned systems are introduced with the framework of linear matrix inequalities (LMIs). Four numerical examples are given to show the improvements over the existing ones and the effectiveness of the proposed methods.

scholarly journals Robust H ∞ state-feedback control for linear systems

2017 ◽  
Vol 473 (2200) ◽  
pp. 20160934 ◽  
Author(s):  
Hao Chen ◽  
Zhenzhen Zhang ◽  
Huazhang Wang
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
Control Algorithm ◽  
State Feedback ◽  
Convex Combination ◽  
State Feedback Control ◽  
Parameter Uncertainties ◽  
Globally Asymptotically Stable ◽  
Loop Control ◽  
Control Approach

This paper investigates the problem of robust H ∞ control for linear systems. First, the state-feedback closed-loop control algorithm is designed. Second, by employing the geometric progression theory, a modified augmented Lyapunov–Krasovskii functional (LKF) with the geometric integral interval is established. Then, parameter uncertainties and the derivative of the delay are flexibly described by introducing the convex combination skill. This technique can eliminate the unnecessary enlargement of the LKF derivative estimation, which gives less conservatism. In addition, the designed controller can ensure that the linear systems are globally asymptotically stable with a guaranteed H ∞ performance in the presence of a disturbance input and parameter uncertainties. A liquid monopropellant rocket motor with a pressure feeding system is evaluated in a simulation example. It shows that this proposed state-feedback control approach achieves the expected results for linear systems in the sense of the prescribed H ∞ performance.

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Global Sensitivity Analysis ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Time Invariant ◽  
The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

Robust model reference control for second-order descriptor linear systems subject to parameter uncertainties

2021 ◽  
pp. 014233122110450
Author(s):  
Guang-Tai Tian ◽  
Guang-Ren Duan
Keyword(s):  
Linear Systems ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Second Order ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Model Reference ◽  
Robust Model ◽  
Robust Compensation ◽  
Descriptor Linear Systems

This paper is devoted to designing the robust model reference controller for uncertain second-order descriptor linear systems subject to parameter uncertainties. The parameter uncertainties are assumed to be norm-bounded. The design of a robust controller can be divided into two separate problems: a robust stabilization problem and a robust compensation problem. Based on the solution of generalized Sylvester matrix equations, we obtain some sufficient conditions to guarantee the complete parameterization of the robust controller. The parametric forms are expressed by a group of parameter vectors which reveal the degrees of freedom existing in the design of the compensator and can be utilized to solve the robust compensation problem. In order to reduce the effect of parameter uncertainties on the tracking error vector, the robust compensation problem is converted into a convex optimization problem with a set of linear matrix equation constraints. A simulation example is provided to illustrate the effectiveness of the proposed technique.

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