Robust Stability Analysis of “Unstructured” Convex Combinations of Matrices With Applications

2006 ◽  
Author(s):  
Rama K. Yedavalli
Keyword(s):  
Stability Analysis ◽  
Robust Stability ◽  
Convex Combination ◽  
Problem Formulation ◽  
Solution Algorithms ◽  
Robust Stability Analysis ◽  
Problem Formulations ◽  
The Stability ◽  
Careful Distinction ◽  
Stable Vertex

This paper presents new insight into the robust stability analysis of families of matrices described by convex combinations of Hurwitz stable 'vertex' matrices. Significant new insight is provided that removes many misconceptions that currently prevail in this problem formulation. In this connection, careful distinction is made between 'Structured' and 'Unstructured' convex combinations of matrices. The convex combinations arising from an uncertain matrix with interval parameters is labeled as 'structured' convex combinations whereas the convex combinations of 'user specified' Hurwitz stable vertex matrices are labeled as 'unstructured' convex combinations. It is clearly shown that the convex combination property in matrix case is dictated more by the nature of the 'vertex' matrices rather than by simply assigning values to the coefficients of the combination. From this analysis, it is clearly established that 'structured' and 'unstructured' convex combinations are two entirely different problem formulations and one is not a special case of the other as it is currently believed. Thus even the solution algorithms for checking the stability of these matrix families are different. After establishing this distinction, this paper then concentrates on the 'unstructured' case and provides a 'vertex solution' to a specific three vertex convex combination problem. The algorithm is illustrated with several examples. This contribution suggests that there is still considerable research needed to appreciably enhance the knowledge base in the important area of robust stability analysis of matrix families which arise in various applications.

scholarly journals Robust Stability Analysis Based on LMI for Haptic Interface Systems with Uncertain Delay

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Yanwen Liu ◽  
Fanwei Meng ◽  
Bowen Guan ◽  
Shuhao Zhang
Keyword(s):  
Stability Analysis ◽  
Robust Stability ◽  
Stability Criterion ◽  
Force Feedback ◽  
Haptic Interface ◽  
Stability Range ◽  
Robust Stability Analysis ◽  
Augmented State ◽  
The Stability ◽  
Environment Parameters

This paper presents the robust stability analysis based on LMI for force feedback haptic interface systems with uncertain delay. A full-order state observer is introduced to estimate states of the haptic device so as to directly obtain the feedback force, which expands the stability range of the system environment parameters when comparing with that of the system without an observer. By using the delay partitioning idea and the augmented state vector, the Lyapunov-Krasovskii functional is constructed, and then the new stability criterion based on LMI is given in the paper. With this new stability criterion, the observer gains can also be obtained directly. At last, a concrete example is used to prove the effectiveness and less conservativeness of this new approach.

scholarly journals Improved Results on Robust Stability Analysis and Stabilization for a Class of Uncertain Nonlinear Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Mohamed Moez Belhaouane ◽  
Mohamed Faiez Ghariani ◽  
Hela Belkhiria Ayadi ◽  
Naceur Benhadj Braiek
Keyword(s):  
Stability Analysis ◽  
Robust Stability ◽  
Polynomial System ◽  
Robust Stabilization ◽  
Polynomial Systems ◽  
System Stability ◽  
Stability Robustness ◽  
Robust Stability Analysis ◽  
The Stability ◽  
Systems Simulation

This paper deals with the problems of robust stability analysis and robust stabilization for uncertain nonlinear polynomial systems. The combination of a polynomial system stability criterion with an improved robustness measure of uncertain linear systems has allowed the formulation of a new criterion for robustness bound estimation of the studied uncertain polynomial systems. Indeed, the formulated approach is extended to involve the global stabilization of nonlinear polynomial systems with maximization of the stability robustness bound. The proposed method is helpful to improve the existing techniques used in the analysis and control for uncertain polynomial systems. Simulation examples illustrate the potentials of the proposed approach.

Robust Stability Analysis of Uncertain Linear Fractional-Order Systems With Time-Varying Uncertainty for 0 < α < 2

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Mohammad Tavazoei ◽  
Mohammad Hassan Asemani
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Robust Stability ◽  
Stability Condition ◽  
Upper Bound ◽  
Order System ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Robust Stability Analysis ◽  
The Stability

This paper focuses on the stability analysis of linear fractional-order systems with fractional-order 0<α<2, in the presence of time-varying uncertainty. To obtain a robust stability condition, we first derive a new upper bound for the norm of Mittag-Leffler function associated with the nominal fractional-order system matrix. Then, by finding an upper bound for the norm of the uncertain fractional-order system solution, a sufficient non-Lyapunov robust stability condition is proposed. Unlike the previous methods for robust stability analysis of uncertain fractional-order systems, the proposed stability condition is applicable to systems with time-varying uncertainty. Moreover, the proposed condition depends on the fractional-order of the system and the upper bound of the uncertainty matrix norm. Finally, the offered stability criteria are examined on numerical uncertain linear fractional-order systems with 0<α<1 and 1<α<2 to verify the applicability of the proposed condition. Furthermore, the stability of an uncertain fractional-order Sallen–Key filter is checked via the offered condition.

Robust Stability Analysis of Interval Fractional-Order Plants with Interval Time delay and General Form of Fractional-Order Controllers

2021 ◽  
pp. 1-1
Author(s):  
Majid Ghorbani ◽  
Mahsan Tavakoli-Kakhki ◽  
Aleksei Tepljakov ◽  
Eduard Petlenkov ◽  
Arash Farnam ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Fractional Order ◽  
Robust Stability ◽  
Interval Time ◽  
Robust Stability Analysis

scholarly journals Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

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