Stability Conditions for a Class of Distributed-Parameter Systems

1966 ◽  
Vol 88 (2) ◽  
pp. 475-479 ◽  
Author(s):  
R. E. Blodgett
Keyword(s):  
Equilibrium State ◽  
Local Stability ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Chemical Reactor ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Stability Conditions ◽  
Stability And Instability ◽  
Liapunov's Direct Method

The purpose of this paper is to obtain stability conditions for a class of nonlinear distributed-parameter systems by using a generalization of Liapunov’s direct method. Sufficient conditions for local stability and instability of the equilibrium state are derived. An application is given in which conditions are obtained for stability of a chemical-reactor process.

scholarly journals Dissipativity-Based Controller Design for Time-Delayed T-S Fuzzy Switched Distributed Parameter Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaona Song ◽  
Mi Wang ◽  
Shuai Song ◽  
Jingtao Man
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Distributed Parameter Systems ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Varying Delay ◽  
Closed Loop Systems ◽  
Control Gain

This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

2020 ◽  
pp. 095965182096689
Author(s):  
Xingyu Zhou ◽  
Haoping Wang ◽  
Yang Tian
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Parabolic Type ◽  
Distributed Parameter Systems ◽  
Temperature Control System ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Stability ◽  
Finite Time Stability ◽  
L2 Norm

In this study, the problem of finite-time stability and boundedness for parabolic singular distributed parameter systems in the sense of [Formula: see text] norm is investigated. First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.

Stability of Cylindrical Shells Under Moving Loads by the Direct Method of Liapunov

1967 ◽  
Vol 34 (4) ◽  
pp. 991-998 ◽  
Author(s):  
G. A. Hegemier
Keyword(s):  
Constant Velocity ◽  
Local Stability ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Functional Space ◽  
Moving Loads ◽  
The Stability ◽  
Shell Axis

The stability of a long, thin, elastic circular cylindrical shell subjected to axial compression and an axisymmetric load moving with constant velocity along the shell axis is studied. With the aid of the direct method of Liapunov, and employing a nonlinear Donnell-type shell theory, sufficient conditions for local stability of the axisymmetric response are established in a functional space whose metric is defined in an average sense. Numerical results, which are presented for the case of a moving decayed step load, reveal that the sufficient conditions for stability developed here and the sufficient conditions for instability obtained in a previous paper lead to the actual stability transition boundary.

GLOBAL STABILITY OF A CHEMOSTAT MODEL WITH DELAYED RESPONSE IN GROWTH AND A LETHAL EXTERNAL INHIBITOR

2008 ◽  
Vol 01 (04) ◽  
pp. 503-520 ◽  
Author(s):  
ZHIQI LU ◽  
JINGJING WU
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Delayed Response ◽  
Qualitative Properties ◽  
Chemostat Model ◽  
Stability And Instability ◽  
Discrete Delays ◽  
Globally Stable

A competition model between two species with a lethal inhibitor in a chemostat is analyzed. Discrete delays are used to describe the nutrient conversion process. The proved qualitative properties of the solution are positivity, boundedness. By analyzing the local stability of equilibria, it is found that the conditions for stability and instability of the boundary equilibria are similar to those in [9]. In addition, the global asymptotic behavior of the system is discussed and the sufficient conditions for the global stability of the boundary equilibria are obtained. Moreover, by numerical simulation, it is interesting to find that the positive equilibrium may be globally stable.

A Procedure for Investigating the Liapunov Stability of Nonautonomous Linear Second-Order Systems

1973 ◽  
Vol 40 (4) ◽  
pp. 1103-1106 ◽  
Author(s):  
S. E. Jones ◽  
T. R. Robe
Keyword(s):  
Differential Equation ◽  
Ad Hoc ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Liapunov Function ◽  
Null Solution ◽  
Liapunov Stability ◽  
The Stability ◽  
Second Order Systems ◽  
Liapunov's Direct Method

Utilizing Liapunov’s direct method a procedure is presented which generates sufficient conditions for the stability of the null solution of the nonautonomous differential equation x¨ + b(t)x˙ + a(t)x = 0. This procedure systematically leads to the construction of a Liapunov function for a given differential equation and thus eliminates the normally ad hoc nature of the direct method. Four examples illustrating the procedure are discussed.

Sign in / Sign up

Export Citation Format

Share Document