scholarly journals Arbitrary Coefficient Assignment by Static Output Feedback for Linear Differential Equations with Non-Commensurate Lumped and Distributed Delays

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2158
Author(s):  
Vasilii Zaitsev ◽  
Inna Kim
Keyword(s):  
Output Feedback ◽  
Sufficient Conditions ◽  
The State ◽  
Distributed Delays ◽  
Static Output Feedback ◽  
Finite Spectrum ◽  
Multiple Variables ◽  
Linear Differential ◽  
Necessary And Sufficient ◽  
Static Output

We consider a linear control system defined by a scalar stationary linear differential equation in the real or complex space with multiple non-commensurate lumped and distributed delays in the state. In the system, the input is a linear combination of multiple variables and its derivatives, and the output is a multidimensional vector of linear combinations of the state and its derivatives. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function by linear static output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for the solvability of the arbitrary coefficient assignment problem by the static output feedback controller. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We provide an example illustrating our results.

scholarly journals Spectrum assignment in linear systems with several commensurate lumped and distributed delays in state by means of static output feedback

2020 ◽  
Vol 56 ◽  
pp. 5-19
Author(s):  
V.A. Zaitsev ◽  
I.G. Kim
Keyword(s):  
Output Feedback ◽  
Assignment Problem ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Static Output Feedback ◽  
Spectrum Assignment ◽  
System A ◽  
Necessary And Sufficient ◽  
Derivatives Of ◽  
Static Output

A linear control system defined by a stationary differential equation of nth order with several commensurate lumped and distributed delays in state is considered. In the system, the input is a linear combination of m variables and their derivatives of order not more than n−p and the output is a k-dimensional vector of linear combinations of the state and its derivatives of order not more than p−1. For this system, a spectrum assignment problem by linear static output feedback with commensurate lumped and distributed delays is studied. Necessary and sufficient conditions are obtained for solvability of the arbitrary spectrum assignment problem by static output feedback controller. Corollaries on stabilization of the system are obtained.

scholarly journals Finite spectrum assignment in linear systems with several lumped and distributed delays by means of static output feedback

2020 ◽  
Vol 30 (3) ◽  
pp. 367-384
Author(s):  
I.G. Kim
Keyword(s):  
Output Feedback ◽  
Assignment Problem ◽  
Closed Loop ◽  
Loop System ◽  
Distributed Delays ◽  
Static Output Feedback ◽  
Closed Loop System ◽  
Finite Spectrum ◽  
Spectrum Assignment ◽  
Static Output

We consider a control system defined by a linear time-invariant system of differential equations with lumped and distributed delays in the state variable. We construct a controller for the system as linear static output feedback with lumped and distributed delays in the same nodes. We study a finite spectrum assignment problem for the closed-loop system. One needs to construct gain coefficients such that the characteristic function of the closed-loop system becomes a polynomial with arbitrary preassigned coefficients. We obtain conditions on coefficients of the system under which the criterion was found for solvability of the finite spectrum assignment problem. Corollaries on stabilization by linear static output feedback with several delays are obtained for the closed-loop system.

DELAY-DEPENDENT H∞ RESILIENT OUTPUT FUZZY CONTROL FOR NONLINEAR DISCRETE-TIME SYSTEMS WITH TIME-DELAY

2011 ◽  
Vol 19 (02) ◽  
pp. 229-250 ◽  
Author(s):  
MOURAD KCHAOU ◽  
AHMED TOUMI ◽  
MANSOUR SOUISSI
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
State Feedback ◽  
Sufficient Conditions ◽  
The State ◽  
System Stability ◽  
Static Output Feedback ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Static Output

This paper is concerned with the problem of non-fragile (resilient) H∞ control for a class of state-delay nonlinear discrete-time systems described by (TS) fuzzy models where both the state feedback and static output feedback are investigated. Based on basis-dependent Lyapunov-krasovskii function, sufficient conditions are derived to achieve the system stability and the H∞ performance. The linear matrix inequality (LMI) approach is proposed to obtain the state-feedback gains, and a homotopy-based iterative LMI algorithm is developed to get the static output feedback gains. An illustrative example shows the effectiveness and the feasibility of the theoretical developments.

THE CONTROLLER DESIGN FOR SINGULAR FRACTIONAL-ORDER SYSTEMS WITH FRACTIONAL ORDER 0 <α< 1

2018 ◽  
Vol 60 (2) ◽  
pp. 230-248
Author(s):  
T. ZHAN ◽  
S. P. MA
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Fractional Order Systems ◽  
Static Output

We study the problem of pseudostate and static output feedback stabilization for singular fractional-order linear systems with fractional order $\unicode[STIX]{x1D6FC}$ when $0<\unicode[STIX]{x1D6FC}<1$. All the results are given by linear matrix inequalities. First, a new sufficient and necessary condition for the admissibility of singular fractional-order systems is presented. Then based on the admissible result, not only are sufficient conditions for designing pseudostate and static output feedback controllers obtained, but also sufficient and necessary conditions are presented by using different methods that guarantee the admissibility of the closed-loop systems. Finally, the effectiveness of the proposed approach is demonstrated by numerical simulations and a real-world example.

scholarly journals Robust Admissibilization of Descriptor Systems by Static Output-Feedback: An LMI Approach

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
M. Chaabane ◽  
F. Tadeo ◽  
D. Mehdi ◽  
M. Souissi
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Initial Value ◽  
Feedback Controllers ◽  
Classical State ◽  
Static Output

The problem of the stabilization of descriptor systems in continuous-time via static output-feedback is studied in this paper and an approach to solve it is proposed. For this, sufficient conditions are derived for the closed-loop system to be admissible (i.e., stable, regular, and impulse-free). These conditions are expressed in terms of a strict Linear Matrix Inequality (LMI); so they are tractable using numerical computations. The proposed controller design methodology is based on two steps: the first is dedicated to synthesizing a classical state-feedback controller, which is used as the initial value for the second step, which uses an LMI problem to obtain static output-feedback controllers that give admissibility. Finally, a numerical example is given to illustrate the results.

scholarly journals Design of Static Output Feedback Controller for Fractional-Order T-S Fuzzy System

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhile Xia
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Matrix Decomposition ◽  
Order Theory ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Feedback Controllers ◽  
Static Output

This paper studies the design of fuzzy static output feedback controllers for two kinds of fractional-order T-S fuzzy systems. The fractional order α satisfies 0<α<1 and 1≤α<2. Based on the fractional order theory, matrix decomposition technique, and projection theorem, four new sufficient conditions for the asymptotic stability of the system and the corresponding controller design methods are given. All the results can be expressed by linear matrix inequalities, and the relationship between fuzzy subsystems is also considered. These have great advantages in solving the results and reducing the conservatism. Finally, a simulation example is given to show the effectiveness of the proposed method.

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