scholarly journals Stability of Sampled-Data Control for Lurie Systems with Slope-Restricted Nonlinearities

2020 ◽  
Author(s):  
Mathias Giordani Titton ◽  
João Manoel Gomes da Silva Jr. ◽  
Giórgio Valmórbida
Keyword(s):  
Continuous Time ◽  
Optimization Problems ◽  
Linear Matrix ◽  
Sampled Data ◽  
Closed Loop System ◽  
Integral Term ◽  
New Class ◽  
Data Control ◽  
The Stability ◽  
Continuous Time System

This paper deals with the stability analysis of aperiodic sampled-data Lurie systems, where the nonlinearity is assumed to be both sector and slope restricted. The proposed method is based on the use of a new class of looped-functionals whose derivative is negative along the trajectories of the continuous-time system. In addition, it contains a generalized Lurie-type function that is quadratic on both the states and the nonlinearity and has a Lurie-Postnikov integral term, which provides some advantages in comparison to simpler candidate functions. On this basis, stability conditions in the form of linear matrix inequalities (LMIs) are formulated. It is shown that the proposed conditions guarantee that the Lurie function is strictly decreasing at the sampling instants, which also implies that the continuous-time trajectories converge asymptotically to the origin. We then formulate some optimization problems for computing themaximal intersampling interval or the maximal sector bounds for which the stability of the sampled-data closed-loop system is guaranteed. A numerical example to illustrate the results is provided.

scholarly journals Study on Bifurcation Analysis and Takagi-Sugeno Fuzzy Sampled-Data Stabilization of PMSM Systems

2021 ◽  
Author(s):  
R Vadivel ◽  
Sabarathinam Srinivasan ◽  
Yongbao Wu ◽  
NALLAPPAN GUNASEKARAN
Keyword(s):  
Fuzzy System ◽  
Permanent Magnet Synchronous Motor ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Sampled Data ◽  
Matlab Toolbox ◽  
New Class ◽  
Data Control ◽  
Delay Dependent ◽  
Takagi Sugeno

The bifurcation, stability and stabilization analysis of permanent magnet synchronous motor (PMSM) systems are investigated in this paper. To begin, a new class of delay-dependent sufficient conditions is suggested with respect to the information of the membership function, a relevant Lyapunov-Krasovskii functional (LKF), and the overall information connected with the real sampling pattern, so that the fuzzy system is ensured to be stable with a weighted dissipativity efficiency. Second, sampled-data control is intended to stabilize the Takagi-Sugeno (T-S) fuzzy system with specified integral inequalities based on the obtained results. The required conditions are stated in terms of the feasibility of linear matrix inequalities (LMIs) under the dissipativity output index, and can readily be verified by MATLAB toolbox. Finally, verification examples are contributed to demonstrated the efficacy of the techniques established in this paper.

scholarly journals Observer-Based Stabilization of Spacecraft Rendezvous with Variable Sampling and Sensor Nonlinearity

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zhuoshi Li ◽  
Ming Liu ◽  
Hamid Reza Karimi ◽  
Xibin Cao
Keyword(s):  
Controller Design ◽  
Sampling Period ◽  
Controller Synthesis ◽  
Linear Matrix ◽  
Sampled Data ◽  
Closed Loop System ◽  
Unified Framework ◽  
Data Control ◽  
Variable Sampling ◽  
Exponentially Stable

This paper addresses the observer-based control problem of spacecraft rendezvous with nonuniform sampling period. The relative dynamic model is based on the classical Clohessy-Wiltshire equation, and sensor nonlinearity and sampling are considered together in a unified framework. The purpose of this paper is to perform an observer-based controller synthesis by using sampled and saturated output measurements, such that the resulting closed-loop system is exponentially stable. A time-dependent Lyapunov functional is developed which depends on time and the upper bound of the sampling period and also does not grow along the input update times. The controller design problem is solved in terms of the linear matrix inequality method, and the obtained results are less conservative than using the traditional Lyapunov functionals. Finally, a numerical simulation example is built to show the validity of the developed sampled-data control strategy.

Exponentially Stable Sampled-Data Control for Uncertain Systems

2014 ◽  
Vol 981 ◽  
pp. 551-554
Author(s):  
Li Ying Fan
Keyword(s):  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Control Input ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Exponentially Stable ◽  
Data Controller ◽  
Continuous Time System

In this paper, the problem of the exponentially stable sampled-data control was investigated for a class of uncertain systems. Based on the input delay approach, the system was modeled as a continuous-time system with the delayed control input. Attention was focused on the design of a state feedback sampled-data controller which guarantees the exponential stability of the closed-loop system for all admissible parametric uncertainties. Using linear matrix inequality (LMI) approach, sufficient conditions are obtained. Simulation example was given to demonstrate the effectiveness and correctness of the proposed method.

scholarly journals Sampled-Data Control of Spacecraft Rendezvous with Discontinuous Lyapunov Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zhuoshi Li ◽  
Ming Liu ◽  
Hamid Reza Karimi ◽  
Xibin Cao
Keyword(s):  
Stability Analysis ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Sampled Data ◽  
Closed Loop System ◽  
Output Tracking ◽  
Output Tracking Control ◽  
Data Control ◽  
Control Scheme ◽  
The Stability

This paper investigates the sampled-data stabilization problem of spacecraft relative positional holding with improved Lyapunov function approach. The classical Clohessy-Wiltshire equation is adopted to describe the relative dynamic model. The relative position holding problem is converted into an output tracking control problem using sampling signals. A time-dependent discontinuous Lyapunov functionals approach is developed, which will lead to essentially less conservative results for the stability analysis and controller design of the corresponding closed-loop system. Sufficient conditions for the exponential stability analysis and the existence of the proposed controller are provided, respectively. Finally, a simulation result is established to illustrate the effectiveness of the proposed control scheme.

scholarly journals On an Application of the Absolute Stability Theory to Sampled-Data Stabilization

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Alexander N. Churilov
Keyword(s):  
Closed Loop ◽  
Control Function ◽  
Linear Matrix ◽  
Feedback Signal ◽  
Matrix Inequality ◽  
Sampled Data ◽  
Closed Loop System ◽  
The Stability ◽  
Absolute Stability Theory ◽  
Sampling Times

A nonlinear Lur’e-type plant with a sector bound nonlinearity is considered. The plant is stabilized by a discrete-time feedback signal with a nonperiodic uncertain sampling. The sampling control function is nonlinear and also obeys some sectoral constraints at discrete (sampling) times. The linear matrix inequality (LMI) conditions for the stability of the closed-loop system are obtained.

scholarly journals Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold

2014 ◽  
Vol 24 (4) ◽  
pp. 745-757 ◽  
Author(s):  
Cheng Zeng ◽  
Shan Liang ◽  
Yuzhe Zhang ◽  
Jiaqi Zhong ◽  
Yingying Su
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Order Term ◽  
Sampling Period ◽  
Approximate Expression ◽  
Relative Degree ◽  
Sampled Data ◽  
Time System ◽  
The Stability ◽  
Continuous Time System

Abstract Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system as power series with respect to a sampling period up to the third order term when the relative degree of the continuous-time system is equal to three, and the corresponding stability of the discretization zeros is discussed for fast sampling rates. Of particular interest are the stability conditions of sampling zeros in the case of a new FROH even though the relative degree of a continuous-time system is greater than two, whereas the conventional FROH fails to do so. An insightful interpretation of the obtained sampled-data model can be made in terms of minimal intersample ripple by design, where multirate sampled systems have a poor intersample behavior. Our results provide a more accurate approximation for asymptotic zeros, and certain known results on asymptotic behavior of limiting zeros are shown to be particular cases of the ideas presented here.

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang
Keyword(s):  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Simulation ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Integration Algorithms ◽  
The Stability ◽  
Continuous Time System

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

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