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LMI conditions for quadratic and robust D-stability of interval systems

控制理论与应用（英文版） 2006年第2期4卷 187-192页

作者： Weijie MAO Xu WANG National Lab of Industrial Control Technology Institute of Advanced Process Control Zhejiang University Hangzhou Zhejiang 310027 China

Sufficient conditions for the quadratic D-stability and further robust D-stability of interval systems are presented in this paper. This robust D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities （LMIs） defined at a series of partial-vertex-based interval matrices other than the total vertex matrices as in previous results. The results contain the usual quadratic and robust stability of continuous-time and discrete-time interval systems as particular cases. The illustrative example shows that this method is effective and less conservative for checking the quadratic and robust D-stability of interval systems.

关键词： interval systems Linear matrix inequality (LMI) Parameter-dependent Lyapunov function Quadratic stability Robust stability

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Stability Margins of MIMO Linear interval systems

Stability Margins of MIMO Linear Interval Systems

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第三十九届中国控制会议

作者： Xindong Li Yu Wang Kui Zou Zhengwei Shi Science and Technology on Space Intelligent Control Laboratory Beijing Institute of Control Engineering

In this paper, a worst-case margin algorithm is proposed to deal with the stability margins of Multi-Input MultiOutput（MIMO） linear time-invariant interval systems. Firstly, the Kharitonov’s Theorem and V. Krishnamurthi’s corollary on Routh criterion are used to prove the stability of MIMO linear interval systems with affine parametric uncertainty structure. In particular, it can be used to analyze the stability regions of interval systems with parameters as well Secondly, each eigenvalue function of the MIMO linear interval systems is regarded as a Single-Input Single-Output（SISO） linear time-invariant *** the frequency domain approach and optimization algorithms are applied to develop a computationally tractable algorithm for calculating the stability margins. Moreover, this method can be extended to the non-minimum phase system. Finally, the engineer relevance examples are presented to validate the effectiveness and accuracy of the proposed method.

关键词： MIMO linear systems stability margin interval systems Kharitonov’s Theorem non-minimum phase system

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The Sliding Mode Variable Structure Control for a Class of interval Distributed Parameter systems with Time-delay

The Sliding Mode Variable Structure Control for a Class of I...

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第二十九届中国控制会议

作者： ZHAO Lin,GAO Cunchen School of Mathematical Sciences,Ocean University of China,Qingdao 266100,P.R.China

The sliding mode control（SMC）problems are researched for a class of interval distributed parameter systems with ***,this system is represented in the distributed parameter systems with parameter uncertainty,and a sufficient condition for robust asymptotically stable is obtained for the sliding mode by constructing Lyapunov functions,employing linear matrix inequality（LMI）.Secondly,a variable structure control（VSC）law is designed,and,the time estimation is given on starting from the initial position of any sate trajectory curve to arrive sliding-model ***,a numerical example is given,and the feasibility and effectiveness of this method is explained.

关键词： interval systems Time-Delay Distributed Parameter systems Sliding mode control LMI

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Positive Observer for Positive Continuous systems with interval Uncertainties and Multiple Time-delay

Positive Observer for Positive Continuous Systems with Inter...

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第24届中国控制与决策会议

作者： Cuihong Wang, Zhaoxia Sheng the Department of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004,China.

This paper addresses the design of positive observer for positive linear continuous system with interval uncertainties and multiple time-delay. Firstly, the sufficient and necessary condition for the existence of positive observers is established by using the vertical matrices of the uncertain domain which system matrices belong to. Then the desired observer matrices are given by solving a set of matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.

关键词： ositive observer time-delay interval systems linear matrix inequalities (LMIs) positive systemositive observer positive systemp

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Design of a robust PID-PSS for an uncertain power system with simplified stability conditions

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Protection and Control of Modern Power systems 2020年第1期5卷 222-237页

作者： Vijaya Lakshmi A.S.V Ramalinga Raju Manyala Siva Kumar Mangipudi Department of EEE G.V.P College of Engineering for WomenVisakhapatnamIndia Department of EEE JNTU KakinadaKakinadaIndia Department of EEE Gudlavalleru Engineering CollegeGudlavalleruAndhra PradeshIndia

In a deregulated power system uncertainty exists and lack of sufficient damping can lead to Low FrequencyOscillations (LFO). The problem can be addressed using robust Power System Stabilizers (PSS). In this paper, anoptimal procedure to design a robust PID-PSS using interval arithmetic for the Single Machine Infinite Bus (SMIB)power system is proposed. The interval modelling captures the wide variations of operating conditions in boundsof system coefficients. In the proposed design procedure, simple and new closed loop stability conditions for anSMIB interval system are developed and are used to design an optimum PID-PSS for improving the performance ofan SMIB system. The optimum PID-PSS is attained by tuning the parameters using the FMINCON tool provided inMATLAB. The robustness of the proposed PID-PSS design is validated and compared to other notable methods inthe literature when the system is subjected to different uncertainties. The simulation results and performance errorvalues show the effectiveness of the proposed robust PID-PSS controller.

关键词： Low frequency oscillations Uncertainty Power system stabilizer Robust controller interval systems

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Finite-time passive control for interval energy-storing electrical circuit model with time-delay and Markov switching

Finite-time passive control for interval energy-storing elec...

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第30届中国控制与决策会议

作者： Shasha Zhu Guici Chen Yali Yang College of Science Wuhan University of Science and Technology

In this paper, we focus on the stochastic finite-time passive control problem for interval energy-storing electrical systems with time-delay and Markov switching. The mathematical model of energy-storing electrical circuit is given firstly, in which not only the error of resistor , inductance and capacitor , but the stochastic disturbance as well are considered. To investigate the finite-time passive control for the interval energy-storing electrical circuit,mathematical model is transformed into a kind of stochastic uncertain systems with time-delay and Markov switching. By constructing a Lyapunov-Krasovskii functional, together with linear matrix inequalities（LMIs） toolbox, some sufficient conditions are given. Meanwhile, the passive controllers are also designed by solving the corresponding LMIs. Naturally,a numerical examples with simulation is given to illustrate the correctness and effectiveness of the designed controller.

关键词： Finite-time passive control interval systems markov switching

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