scholarly journals Convergent Properties of Riccati Equation with Application to Stability Analysis of State Estimation

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
X. Cai ◽  
Y. S. Ding ◽  
S. Y. Li
Keyword(s):  
Stability Analysis ◽  
State Estimation ◽  
Kalman Filters ◽  
Sufficient Conditions ◽  
Time Instant ◽  
Novel Method ◽  
Finite Memory ◽  
The Stability ◽  
Time Invariant ◽  
Selection Of

Since the recursive nature of Kalman filtering always results in a growing size of the optimization problem, state estimation is usually realized by use of finite-memory, receding horizon, sliding window, or “frozen” techniques, which causes difficulties on stability analysis. This paper proposes a novel method on selection of an initial covariance matrix and a horizon for the Kalman filter to make sure that a sequence of the closed-loop Kalman filters are stable as time-invariant filters at subsequent time instant. Convergent properties of Riccati Difference Equation (RDE) are first exploited. Based on these properties, sufficient conditions for stability of a sequence of Kalman filters are obtained. Compared with the existent literature, the convergent properties and the stability conditions are less conservative since they provide analytic results and are applicable to more common cases where the RDEs are not monotonic.

Stability and controllability of switched systems

2013 ◽  
Vol 61 (3) ◽  
pp. 547-555 ◽  
Author(s):  
J. Klamka ◽  
A. Czornik ◽  
M. Niezabitowski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Arbitrary Switching ◽  
Mathematical Problems ◽  
The Stability ◽  
Necessary And Sufficient

Abstract The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After that, we review the controllability results.

Lyapunov-Based Sufficient Conditions for Nonlinear Impulsive Systems

2011 ◽  
Vol 219-220 ◽  
pp. 508-512
Author(s):  
Yong Liang Gao ◽  
Xiao Wu Mu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Invariant Set ◽  
Positive Definite ◽  
Impulsive Systems ◽  
Stability Theorems ◽  
Sufficient Conditions For Convergence ◽  
The Stability

This paper focuses on the stability analysis and invariant set stability theorems for nonlinear impulsive systems. A set of Lyapunov-based sufficient conditions are established for these convergent properties. These results do not require the Lyapunov function to be positive definite. Inequalities relating the righthandside of the differential equation and the Lyapunov function derivative are involved for these results. These inequalities make it possible to deduce properties of the functions and thus leads to sufficient conditions for convergence and stability.

scholarly journals On uniform asymptotic stability for nonlinear integro-differential equations of Volterra type

2019 ◽  
pp. 161-166
Author(s):  
Natalia Sedova
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Auxiliary Function ◽  
Uniform Asymptotic Stability ◽  
Volterra Type ◽  
Razumikhin Technique ◽  
The Stability ◽  
The Right

The specifics of the application of Razumikhin technique to the stability analysis of Volterra type integrodifferential equations are considered. The equation can be nonlinear and nonautonomous. We propose new sufficient conditions for uniform asymptotic stability of the zero solution using the phase space of a special construction and constraints on the right side of the equation. In the presented constraints we can analyze stability, relying not only on the behavior of the auxiliary function along the solutions, but also on the properties of the so called limiting equations.

scholarly journals Computation of time-delay for Delayed Network Controlled Temperature Control System

2021 ◽  
Vol 2070 (1) ◽  
pp. 012102
Author(s):  
V Venkatachalam ◽  
M Ramasubramanian ◽  
M Thirumarimurugan ◽  
D Prabhakaran
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Temperature Control ◽  
Closed Loop ◽  
Simulation Software ◽  
Loop System ◽  
Temperature Control System ◽  
Closed Loop System ◽  
The Stability ◽  
Time Invariant

Abstract This paper presents an Investigation on the stability of network controlled temperature control system having Time-Invariant feedback delays, by utilizing a direct method for TDS stability analysis. A PI controller based stability analysis for temperature control system with Time invariant feedback loop delay has been constructed in this paper. The stability problem has been formulated based on the transfer function model of the closed loop system with various time delays. For different subsets of the controller parameters, based on the stability criterion’s maximal permissible bound of the network link delay that the closed loop system can accommodate without losing the stability has been computed. The effectiveness of the obtained result was validated on a benchmark temperature control system using MATLAB simulation software.

scholarly journals Common Weak Linear Copositive Lyapunov Functions for Positive Switched Linear Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yuangong Sun ◽  
Zhaorong Wu ◽  
Fanwei Meng
Keyword(s):  
Stability Analysis ◽  
Complex Systems ◽  
Linear Systems ◽  
Algebraic Structure ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

Lyapunov functions play a key role in the stability analysis of complex systems. In this paper, we study the existence of a class of common weak linear copositive Lyapunov functions (CWCLFs) for positive switched linear systems (PSLSs) which generalize the conventional common linear copositive Lyapunov functions (CLCLFs) and can be used as handy tool to deal with the stability of PSLSs not covered by CLCLFs. We not only establish necessary and sufficient conditions for the existence of CWCLFs but also clearly describe the algebraic structure of all CWCLFs. Numerical examples are also given to demonstrate the effectiveness of the obtained results.

scholarly journals Semistability of Nonlinear Impulsive Systems with Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Xiaowu Mu ◽  
Yongliang Gao
Keyword(s):  
Stability Analysis ◽  
Hybrid System ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Impulsive Systems ◽  
Stability Properties ◽  
System Energy ◽  
The Stability ◽  
Storage Energy

This paper is concerned with the stability analysis and semistability theorems for delay impulsive systems having a continuum of equilibria. We relate stability and semistability to the classical concepts of system storage functions to impulsive systems providing a generalized hybrid system energy interpretation in terms of storage energy. We show a set of Lyapunov-based sufficient conditions for establishing these stability properties. These make it possible to deduce properties of the Lyapunov functional and thus lead to sufficient conditions for stability and semistability. Our proposed results are evaluated using an illustrative example to show their effectiveness.

A New Approach to Popov Criterion for Stability Analysis of Nonlinear Control Systems

2012 ◽  
Vol 463-464 ◽  
pp. 1549-1552
Author(s):  
Ivan Svarc
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Nonlinear Control ◽  
Control Systems ◽  
Transfer Functions ◽  
Sufficient Conditions ◽  
Nonlinear Control Systems ◽  
Engineering Practice ◽  
The Stability ◽  
The Given

The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The tables includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically. Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.

scholarly journals Asymptotic Stability Analysis and Optimality Algorithm for Uncertain Neutral Systems with Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Xinghua Liu
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
The Novel ◽  
Neutral Systems ◽  
Additive Decomposition ◽  
Decomposition Approach ◽  
Optimality Algorithm ◽  
The Stability ◽  
The Relationship

The certain and uncertain neutral systems with time-delay and saturating actuator are considered in this paper. In order to analyse and optimize the system, auxiliary functions are presented based on additive decomposition approach and the relationship among them is discussed. As the novel stability criterion, two sufficient conditions are obtained for asymptotic stability of the neutral systems. Furthermore, the paper gives the stability analysis algorithm and optimality algorithm to optimize the result. Finally, from the two-stage dissolution tank of solid caustic soda in a chemical plant, three numerical examples are implemented to show the effectiveness of the proposed method.

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