Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions

This paper addresses the stability and stabilization of discrete switched systems which can be used to describe manufacturing systems. A new sufficient and necessary condition in the use of parameter-dependent Lyapunov functions is proposed to guarantee the switched system stability under arbitrary switching. The control synthesis approach presented in this work reduces the conservatism by slack variables while investigating the static output feedback control issue. A cone complementarity linearization algorithm is applied to make the condition a minimization problem in the form of LMIs. By numerical evaluation, the new control design technique is illustrated to be more efficient.

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Improved stability and stabilization conditions for Takagi-Sugeno fuzzy systems via fuzzy lyapunov functions

2013 25th Chinese Control and Decision Conference (CCDC) ◽

10.1109/ccdc.2013.6561471 ◽

2013 ◽

Author(s):

Guojun Liu

Keyword(s):

Lyapunov Functions ◽

Fuzzy Systems ◽

Improved Stability ◽

Stability And Stabilization ◽

Takagi Sugeno

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Vector Lyapunov functions for stability and stabilization of differential repetitive processes

Journal of Computer and Systems Sciences International ◽

10.1134/s1064230716040067 ◽

2016 ◽

Vol 55 (4) ◽

pp. 503-514 ◽

Cited By ~ 9

Author(s):

K. Galkowski ◽

M. A. Emelianov ◽

P. V. Pakshin ◽

E. Rogers

Keyword(s):

Lyapunov Functions ◽

Repetitive Processes ◽

Vector Lyapunov Functions ◽

Stability And Stabilization

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Global exponential stabilization of nonlinear systems via width time-dependent periodically intermittent smooth control

Advances in Difference Equations ◽

10.1186/s13662-020-02969-3 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Jitai Liang ◽

Wanjun Xia

Keyword(s):

Nonlinear Systems ◽

Lyapunov Functions ◽

Exponential Convergence ◽

Sufficient Conditions ◽

Time Dependent ◽

Smooth Control ◽

Index Function ◽

Stability And Stabilization ◽

In Virtue Of ◽

Theoretical Results

Abstract In this paper, the global exponential stability and stabilization problems for a class of nonlinear systems are investigated. Some sufficient conditions to guarantee global exponential stable and estimate the minimum admissible value of the control width are presented in virtue of time-dependent width Lyapunov functions. Furthermore, a periodically intermittent smooth controller with variant control width is introduced and theoretical analysis is provided. The smooth index function of periodically intermittent smooth control inputs is defined and the supremum (or least upper bound) of smooth index function set can be solved. On the basis of the analysis, the designed periodically intermittent smooth controller not only can globally exponentially stabilize the nonlinear systems, but also can control the exponential convergence rate of the nonlinear systems. Finally, numerical simulations are given to verify the obtained theoretical results.

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