scholarly journals On exponential dichotomy in Banach spaces

1981 ◽  
Vol 23 (2) ◽  
pp. 293-306 ◽  
Author(s):  
Mihail Megan ◽  
Petre Preda
Keyword(s):  
Banach Space ◽  
Control Systems ◽  
Linear Systems ◽  
Banach Spaces ◽  
Exponential Dichotomy ◽  
Linear Control ◽  
Linear Control Systems

In this paper we study the exponential dichotomy property for linear systems, the evolution of which can be described by a semigroup of class C0 on a Banach space. We define the class of (p, q) dichotomic semigroups and establish the connections between the dichotomy concepts and admissibility property of the pair (Lp, Lq) for linear control systems. The obtained results are generalizations of well-known results of W.A. Coppel, J.L. Massera and J.J. Schäffer, K.J. Palmer.

scholarly journals On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sendren Sheng-Dong Xu ◽  
Chih-Chiang Chen
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Switched Systems ◽  
The Other ◽  
Linear Control ◽  
Linear Control Systems ◽  
Problem Statement ◽  
Theoretical Derivation ◽  
Control Laws ◽  
Numerical Examples

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

scholarly journals Measurable multifunctions and their applications to convex integral functionals

1989 ◽  
Vol 12 (1) ◽  
pp. 175-191 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Control Systems ◽  
Banach Spaces ◽  
Time Dependent ◽  
Linear Control ◽  
Linear Control Systems ◽  
Integral Functionals ◽  
Control Constraints ◽  
Infinite Dimensional ◽  
Measurable Multifunctions

The purpose of this paper is to establish some new properties of set valued measurable functions and of their sets of Integrable selectors and to use them to study convex integral functionals defined on Lebesgue-Bochner spaces. In this process we also obtain a characterization of separable dual Banach spaces using multifunctions and we present some generalizations of the classical “bang-bang” principle to infinite dimensional linear control systems with time dependent control constraints.

Pseudo-Hopf Bifurcation for a Class of 3D Filippov Linear Systems

2021 ◽  
Vol 31 (02) ◽  
pp. 2150025
Author(s):  
José Manuel Islas ◽  
Juan Castillo ◽  
Baltazar Aguirre-Hernandez ◽  
Fernando Verduzco
Keyword(s):  
Hopf Bifurcation ◽  
Control Systems ◽  
Linear Systems ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Linear Control ◽  
Linear Control Systems ◽  
The Family

We consider a nongeneric family of 3D Filippov linear systems with a discontinuity plane that have two parallel tangency lines, such that the region between them is the sliding region. We are interested in finding under what conditions the family has a crossing limit cycle, when the sliding region changes its stability. We call this phenomenon the pseudo-Hopf bifurcation. This class of systems is motivated by piecewise-linear control systems which have not yet been treated in the context of crossing limit cycles.

scholarly journals Structural Controllability of Discrete-Time Linear Control Systems with Time-Delay: A Delay Node Inserting Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Ailing Qi ◽  
Xuewei Ju ◽  
Qing Zhang ◽  
Zengqiang Chen
Keyword(s):  
Time Delay ◽  
Control Systems ◽  
Linear Systems ◽  
Discrete Time ◽  
Linear Control ◽  
Linear Control Systems ◽  
Structural Controllability ◽  
Time Linear ◽  
Theoretical Results

This paper is concerned with the structural controllability analysis for discrete-time linear control systems with time-delay. By adding virtual delay nodes, the linear systems with time-delay are transformed into corresponding linear systems without time-delay, and the structural controllability of them is equivalent. That is to say, the time-delay does not affect or change the controllability of the systems. Several examples are also presented to illustrate the theoretical results.

Fractional Vector-Order h-Realisation of the Impulse Response Function

2020 ◽  
Vol 14 (2) ◽  
pp. 108-113
Author(s):  
Ewa Pawłuszewicz
Keyword(s):  
Control Systems ◽  
Impulse Response ◽  
Response Function ◽  
Impulse Response Function ◽  
Linear Control ◽  
Linear Control Systems

AbstractThe problem of realisation of linear control systems with the h–difference of Caputo-, Riemann–Liouville- and Grünwald–Letnikov-type fractional vector-order operators is studied. The problem of existing minimal realisation is discussed.

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