ON THE STABILITY RADIUS OF SWITCHED POSITIVE LINEAR SYSTEMS

2020 ◽  
pp. 90-98
Author(s):  
Ngoc
Keyword(s):  
Lower Bound ◽  
Linear Systems ◽  
Upper Bound ◽  
Lyapunov Functional ◽  
Stability Radius ◽  
Exponentially Stable ◽  
The Stability

This article investigates the stability radius based on exponentially stable of switched positive linear systems. A lower bound and upper bound for this radius with respect to structured affine positive perturbations of the system's parameters are established under the assumption that all its positive subsystems have a common linear copositive Lyapunov functional. An example is provided for illustrating the result.

scholarly journals Robust Stability of Time-Varying Markov Jump Linear Systems with Respect to a Class of Structured, Stochastic, Nonlinear Parametric Uncertainties

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 148
Author(s):  
Vasile Dragan ◽  
Samir Aberkane
Keyword(s):  
Lower Bound ◽  
Linear Systems ◽  
Robust Stability ◽  
Stability Radius ◽  
Control Synthesis ◽  
Parametric Uncertainties ◽  
Jump Linear Systems ◽  
Markov Jump Linear Systems ◽  
Robust Stability Analysis ◽  
The Stability

This note is devoted to a robust stability analysis, as well as to the problem of the robust stabilization of a class of continuous-time Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations. The considered parametric uncertainties are of multiplicative white noise type with unknown intensity. In order to effectively address the multi-perturbations case, we use scaling techniques. These techniques allow us to obtain an estimation of the lower bound of the stability radius. A first characterization of a lower bound of the stability radius is obtained in terms of the unique bounded and positive semidefinite solutions of adequately defined parameterized backward Lyapunov differential equations. A second characterization is given in terms of the existence of positive solutions of adequately defined parameterized backward Lyapunov differential inequalities. This second result is then exploited in order to solve a robust control synthesis problem.

On Buckling Loads of Timoshenko Columns with Elastically Supported Ends

2012 ◽  
Vol 446-449 ◽  
pp. 578-581
Author(s):  
Hua Zhang ◽  
Xiang Fang Li
Keyword(s):  
Lower Bound ◽  
Closed Form ◽  
Upper Bound ◽  
Intermediate State ◽  
Critical Loads ◽  
Compressive Force ◽  
Buckling Loads ◽  
Characteristic Equations ◽  
The Stability ◽  
Elastically Supported

The stability of Timoshenko columns with elastically supported ends under axially compressive force is analyzed. Characteristic equations are obtained according to an intermediate state between Haringx’s and Engesser’s models. For clamped-free, clamped-clamped, and pinned-pinned columns, buckling loads are given in closed form. The influences of elastic restraint stiffness on the critical loads are elucidated. Haringx’s and Engesser’s models are two extreme cases of the present. Critical buckling loads using Haringx’s model are upper bound, and those using Engesser’s model are lower bound.

scholarly journals Sharp Bounds on the Spectral Radius of Nonnegative Matrices and Comparison to the Frobenius’ Bounds

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Discrete Time ◽  
Upper Bound ◽  
Nonnegative Matrix ◽  
Nonnegative Matrices ◽  
Sharp Bounds ◽  
Similarity Transformations ◽  
Linear Invariant ◽  
The Stability

In this paper, a new upper bound and a new lower bound for the spectral radius of a nοnnegative matrix are proved by using similarity transformations. These bounds depend only on the elements of the nonnegative matrix and its row sums and are compared to the well-established upper and lower Frobenius’ bounds. The proposed bounds are always sharper or equal to the Frobenius’ bounds. The conditions under which the new bounds are sharper than the Frobenius' ones are determined. Illustrative examples are also provided in order to highlight the sharpness of the proposed bounds in comparison with the Frobenius’ bounds. An application to linear invariant discrete-time nonnegative systems is given and the stability of the systems is investigated. The proposed bounds are computed with complexity O(n2).

scholarly journals H∞Control for a Networked Control Model of Systems with Two Additive Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hanyong Shao ◽  
Zhengqiang Zhang ◽  
Xunlin Zhu ◽  
Guoying Miao
Keyword(s):  
Upper Bound ◽  
Lyapunov Functional ◽  
Control Method ◽  
Control Model ◽  
Networked Control ◽  
Disturbance Attenuation ◽  
Time Varying ◽  
Stability Criteria ◽  
The Stability ◽  
Polyhedron Method

This paper is concerned withH∞control for a networked control model of systems with two additive time-varying delays. A new Lyapunov functional is constructed to make full use of the information of the delays, and for the derivative of the Lyapunov functional a novel technique is employed to compute a tighter upper bound, which is dependent on the two time-varying delays instead of the upper bounds of them. Then the convex polyhedron method is proposed to check the upper bound of the derivative of the Lyapunov functional. The resulting stability criteria have fewer matrix variables but less conservatism than some existing ones. The stability criteria are applied to designing a state feedback controller, which guarantees that the closed-loop system is asymptotically stable with a prescribedH∞disturbance attenuation level. Finally examples are given to show the advantages of the stability criteria and the effectiveness of the proposed control method.

An Upper Bound on the Maximum Stability Radius Achievable by State Feedback

2005 ◽  
Vol 128 (3) ◽  
pp. 718-721 ◽  
Author(s):  
R. Rajamani ◽  
Y. M. Cho
Keyword(s):  
Upper Bound ◽  
State Feedback ◽  
Closed Loop ◽  
Stability Radius ◽  
Feedback Matrix ◽  
Maximum Stability ◽  
Loop Matrix ◽  
The Stability

In this paper we relate the stability radius that can be achieved for the closed-loop matrix (A−BK) to the distance to unstabilizability of the pair (A,B). In the paper we show that the closed-loop matrix (A−BK) can achieve a stability radius of γ with a real feedback matrix K only if the distance to unstabilizability of (A,B) is greater than γ. Thus the distance to the unstabilizability of (A,B) provides an upper bound on the maximum stability radius that can be achieved by state feedback.

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