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A computing capability test for a switched system control design using the Haris-Rogers method

Journal of Zhejiang University-Science C(Computers and Electronics) 2012年第10期13卷 781-792页

作者： Mohd Amin AT-TASNEEM Sallehuddin Mohamed HARIS Zulkifli Mohd NOPIAH Faculty of Mechanical Engineering University Malaysia Pahang Pekan 26600 Malaysia Department of Mechanical and Materials Engineering Faculty of Engineering and the Built Environment Universiti Kebangsaan Malaysia UKM Bangi 43600 Malaysia Unit of Fundamental Engineering Studies Faculty of Engineering and the Built Environment Universiti Kebangsaan Malaysia UKM Bangi 43600 Malaysia

The problem of finding stabilizing controllers for switched systems is an area of much research interest as conventional concepts from continuous time and discrete event dynamics do not hold true for these *** solutions have been proposed,most of which are based on finding the existence of a common lyapunov function(CLF) or a multiple lyapunov function(MLF) where the key is to formulate the problem into a set of linear matrix inequalities(LMIs).An alternative method for finding the existence of a CLF by solving two sets of linear inequalities(LIs) has previously been *** method is seen to be less computationally taxing compared to methods based on solving *** substantiate this,the computational ability of three numerical computational solvers,LMI solver,cvx,and Yalmip,as well as the symbolic computational program Maple were tested.A specific switched system comprising four second-order subsystems was used as a test *** the obtained solutions,the validity of the controllers and the corresponding CLF was *** was found that all tested solvers were able to correctly solve the *** issue of rounding-off error in numerical computation based software is discussed in *** test revealed that the guarantee of stability became uncertain when the rounding off was at a different decimal *** use of different external solvers led to the same conclusion in terms of the stability of switched *** a result,a shift from using a conventional numerical computation based program to using computer algebra is suggested.

关键词： Linear inequalities Hybrid systems Stability common quadratic lyapunov function Numerical computation Symbolic computation

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Construction of common quadratic lyapunov functions

Construction of Common Quadratic Lyapunov Functions

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第二十四届中国控制会议

作者： Yahong Zhu, Huashu Qin Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, P.R.China

＜正＞ When a set of stable matrices are commutative, Narendra and Balakrishnan proposed a way to construct a common quadratic lyapunov function （CQLF） [8]. This paper explores the conditions, under which the method can also be used for certain non-commutative sets. First, for two dimensional Lie algebra, a sufficient condition is provided for constructing a CQLF. The method is also extended to non-involutive case. Then the general case is considered, under certain condition the structure remains available. Next, the problem when a stable matrix can be added to a set of matrices with CQLF and construct a new CQLF for the enlarged set.

关键词： Switched system common quadratic lyapunov function Lie algebra

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quadratic stabilization of switched nonlinear systems

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Science in China(Series F) 2009年第6期52卷 999-1006页

作者： DONG YaLi FAN JiaoJiao MEI ShengWei School of Science Tianjin Polytechnic University Tianjin 300160 China Department of Electrical Engineering Tsinghua University Beijing 100084 China

In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is *** switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching *** results of this paper are also applied to switched linear systems.

关键词： switched nonlinear system quadratic stabilization uniform normal form zero dynamics common quadratic lyapunov function

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Stability and Stabilization of Block-cascading Switched Linear Systems

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International Journal of Automation and computing 2006年第4期3卷 404-413页

作者： Ya-Hong Zhu Dai-Zhang Cheng Institute of Systems Science Chinese Academy of Sciences Beijing PRC

The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the common cascading form, a common quadratic lyapunov function is （QLFs） is explored by finding common QLFs of diagonal blocks. In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.

关键词： Switching linear system quadratic stability common quadratic lyapunov function reducible Lie algebra,cascading Quaker Lemma

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Stabilization of a Class of Switched Systems with Unstabilizable Switchin Modes

Stabilization of a Class of Switched Systems with Unstabiliz...

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第25届中国控制会议

作者： Zhu Yahong, Cheng Daizhan Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080

＜正＞This paper considers the stabilization of a class of switched control systems. Every switching mode is assumed to be not stabilizable. First, the linear case is considered. Assume the switching strategy and control are designable, a new stabilization technique is proposed, which stabilizes the unstabilizable sub-system by proper switching strategy and then stabilizes the stabilizable sub-system by using common quadratic lyapunov function approach to the closed-loop sub-system. An easily verifiable sufficient condition is obtained. An illustrative example is provided to demonstrate the design procedure. Then using lyapunov function with homogeneous derivative, similar design technique is used to stabilize switched nonlinear systems.

关键词： Switched control system Exponential stability common quadratic lyapunov function lyapunov function with homogeneous derivative.

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On quadratic lyapunov function of Planar Systems

On Quadratic Lyapunov Function of Planar Systems

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第二十届中国控制会议

作者： Daizhan Cheng Institute of Systems Science, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing 100080, P.R.China

＜正＞This paper considers the problem of finding a common quadratic lyapunov function for a set of planar systems. The main contribution of this paper is to figure out the set of quadratic lyapunov functions for a given stable planar system. Then a necessary and sufficient condition for a set of plane systems to share a common quadratic lyapunov function is obtained consequently. It is not only easily verifiable but also constructive. It provides a method to construct all common quadratic lyapunov functions. As an application, higher dimensional cases are also considered.

关键词： Switch system common quadratic lyapunov function orthogonal transformation solvable Lie algebra quasi-flag

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Set Stability and Controllability for Switched Nonhomogeneous Linear Systems

Set Stability and Controllability for Switched Nonhomogeneou...

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第25届中国控制会议

作者： Cheng Daizhan,Hu Xiaoming Institute of Systems Science, AMSS,Chinese Academy of Sciences,Beijing 100080,P. R. China Optimization and Systems Theory, Royal Institute of Technology,Stockholm, Sweden

＜正＞In this paper we consider some control problems of switched non-homogeneous linear systems. First,the set stability of switched non-homogeneous linear systems is considered. It is proved that as the linear parts have a common quadratic lyapunov function the set stability is assured. The problem of searching smallest attracting set is then considered. Then we assume the switching law is controllable and investigate the controllability condition within the attracting region. Finally, we consider the aggregation and the control of aggregation of fiocking behavior. Particularly,the results obtained are implemented to analyzing and manipulating of a group of mobile robots.

关键词： Switched system Set Stability common quadratic lyapunov function Controllability

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Stability Analysis of Unified Chaotic Systems via Switching Control

Stability Analysis of Unified Chaotic Systems via Switching ...

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第36届中国控制会议

作者： Changchun Sun Xin Jing Shenyang Jianzhu University

ISBN: (纸本)9781538629185

The problem on the existence of a common quadratic lyapunov function for switched unified chaotic systems is investigated in this paper. Switched unified chaotic systems with a varying parameter are constructed. A sufficient condition on the existence of a common quadratic lyapunov function is derived in view of the solution to a group of matrix inequalities. By designing linear state feedback controllers, the controlled switched unified chaotic systems can be asymptotically stable via arbitrary switching. Finally, a random numerical example and its simulations illustrate the effectiveness of the switching control approach.

关键词： switched unified chaotic systems common quadratic lyapunov function switching control chaotic attractor

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