A class of robust stability conditions where linear parameter dependence of the Lyapunov function is a necessary condition for arbitrary parameter dependence

2005 ◽  
Vol 54 (11) ◽  
pp. 1131-1134 ◽  
Author(s):  
M.C. de Oliveira ◽  
J.C. Geromel
Keyword(s):  
Lyapunov Function ◽  
Robust Stability ◽  
Parameter Dependence ◽  
Necessary Condition ◽  
Arbitrary Parameter ◽  
Stability Conditions ◽  
Linear Parameter

scholarly journals LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
A. Hmamed ◽  
M. Alfidi ◽  
A. Benzaouia ◽  
F. Tadeo
Keyword(s):  
Lyapunov Function ◽  
Robust Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Polytopic Uncertainty ◽  
Matrix Inequalities ◽  
Discrete Time Systems ◽  
Parameter Dependent ◽  
Time Systems

Robust stability conditions are derived for uncertain 2D linear discrete-time systems, described by Fornasini-Marchesini second models with polytopic uncertainty. Robust stability is guaranteed by the existence of a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope. Several examples are presented to illustrate the results.

scholarly journals Iterative stability analysis for general polynomial control systems

2021 ◽  
Author(s):  
Bo Xiao ◽  
Hak-Keung Lam ◽  
Zhixiong Zhong
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Control Systems ◽  
Polynomial System ◽  
Stability Conditions ◽  
General Polynomial ◽  
Main Challenge ◽  
Detailed Simulation ◽  
Feasible Solutions ◽  
The Stability

AbstractThe main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.

scholarly journals Lyapunov Analysis of Two Imbalanced Power System Areas

2021 ◽  
Vol 19 (3) ◽  
Author(s):  
Gilang Nugraha Putu Pratama ◽  
Adha Imam Cahyadi
Keyword(s):  
Lyapunov Function ◽  
Transmission Lines ◽  
Transient Stability ◽  
Analytical Tool ◽  
Necessary Condition ◽  
Lyapunov Analysis ◽  
Simultaneous Solution ◽  
Region Of Attraction ◽  
Admittance Matrix ◽  
Clearing Time

The transient stability is the capability of the system to preserve synchronism while being affected by large disturbances. It is a nonlinear problem that requires a simultaneous solution for many differential equations. Therefore, a thorough analysis is needed to resolve it. In this paper, we present the transient stability for multimachine under different fault cases and to analyze using the Lyapunov function. It serves as an analytical tool to determine the necessary condition to be stable. The system is stable as long as it is contained in the region of attraction. Meanwhile, the swing equation and reduced admittance matrix are used to model the system in three conditions, pre-fault, during the fault, and post-fault. The numerical simulations are conducted to verify that the synchronism can be preserved despite under faults on the transmission lines by achieving the critical clearing time.  

scholarly journals Estimating kinetic mechanisms with prior knowledge II: Behavioral constraints and numerical tests

2018 ◽  
Vol 150 (2) ◽  
pp. 339-354 ◽  
Author(s):  
Marco A. Navarro ◽  
Autoosa Salari ◽  
Mirela Milescu ◽  
Lorin S. Milescu
Keyword(s):  
Prior Knowledge ◽  
Estimation Procedure ◽  
Kinetic Mechanism ◽  
Arbitrary Parameter ◽  
Linear Parameter ◽  
Open Probability ◽  
Behavioral Constraints ◽  
Kinetic Mechanisms ◽  
Mathematical Relationships ◽  
Optimization Mechanism

Kinetic mechanisms predict how ion channels and other proteins function at the molecular and cellular levels. Ideally, a kinetic model should explain new data but also be consistent with existing knowledge. In this two-part study, we present a mathematical and computational formalism that can be used to enforce prior knowledge into kinetic models using constraints. Here, we focus on constraints that quantify the behavior of the model under certain conditions, and on constraints that enforce arbitrary parameter relationships. The penalty-based optimization mechanism described here can be used to enforce virtually any model property or behavior, including those that cannot be easily expressed through mathematical relationships. Examples include maximum open probability, use-dependent availability, and nonlinear parameter relationships. We use a simple kinetic mechanism to test multiple sets of constraints that implement linear parameter relationships and arbitrary model properties and behaviors, and we provide numerical examples. This work complements and extends the companion article, where we show how to enforce explicit linear parameter relationships. By incorporating more knowledge into the parameter estimation procedure, it is possible to obtain more realistic and robust models with greater predictive power.

Sign in / Sign up

Export Citation Format

Share Document