Sufficient conditions for simultaneous stabilization of three linear systems within the framework of nest algebras

2014 ◽  
Vol 351 (12) ◽  
pp. 5310-5325 ◽  
Author(s):  
Tianqiu Yu ◽  
Wei Chi
Keyword(s):  
Linear Systems ◽  
Sufficient Conditions ◽  
Simultaneous Stabilization ◽  
Nest Algebras

scholarly journals Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

2012 ◽  
Vol 22 (4) ◽  
pp. 451-465 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Diagram Method ◽  
State Variable ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.

scholarly journals On the solvability of the modified Cauchy problem for linear systems of generalized ordinary differential equations with singularities

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Malkhaz Ashordia ◽  
Inga Gabisonia ◽  
Mzia Talakhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Unique Solvability ◽  
Sufficient Conditions ◽  
The Cauchy Problem ◽  
Generalized Ordinary Differential Equations

AbstractEffective sufficient conditions are given for the unique solvability of the Cauchy problem for linear systems of generalized ordinary differential equations with singularities.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

Rank-one LMI approach to simultaneous stabilization of linear systems

1999 ◽  
Vol 38 (2) ◽  
pp. 79-89 ◽  
Author(s):  
Didier Henrion ◽  
Sophie Tarbouriech ◽  
Michael Šebek
Keyword(s):  
Linear Systems ◽  
Simultaneous Stabilization ◽  
Lmi Approach ◽  
Rank One

scholarly journals Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems

2007 ◽  
Vol 50 (5) ◽  
pp. 719-731 ◽  
Author(s):  
Qiang Guan ◽  
Long Wang ◽  
BiCan Xia ◽  
Lu Yang ◽  
WenSheng Yu ◽  
...  
Keyword(s):  
Linear Systems ◽  
Simultaneous Stabilization

scholarly journals Computation of positive realization of MIMO hybrid linear systems in the form of second Fornasini-Marchesini model

2010 ◽  
Vol 20 (3) ◽  
pp. 267-285 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Linear Systems ◽  
Hybrid Systems ◽  
Transfer Matrix ◽  
Sufficient Conditions ◽  
The State ◽  
Realization Problem ◽  
Numerical Example ◽  
State Variable

Computation of positive realization of MIMO hybrid linear systems in the form of second Fornasini-Marchesini modelThe realization problem for positive multi-input and multi-output (MIMO) linear hybrid systems with the form of second Fornasini-Marchesini model is formulated and a method based on the state variable diagram for finding a positive realization of a given proper transfer matrix is proposed. Sufficient conditions for the existence of the positive realization of a given proper transfer matrix are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.

Robust model reference control for second-order descriptor linear systems subject to parameter uncertainties

2021 ◽  
pp. 014233122110450
Author(s):  
Guang-Tai Tian ◽  
Guang-Ren Duan
Keyword(s):  
Linear Systems ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Second Order ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Model Reference ◽  
Robust Model ◽  
Robust Compensation ◽  
Descriptor Linear Systems

This paper is devoted to designing the robust model reference controller for uncertain second-order descriptor linear systems subject to parameter uncertainties. The parameter uncertainties are assumed to be norm-bounded. The design of a robust controller can be divided into two separate problems: a robust stabilization problem and a robust compensation problem. Based on the solution of generalized Sylvester matrix equations, we obtain some sufficient conditions to guarantee the complete parameterization of the robust controller. The parametric forms are expressed by a group of parameter vectors which reveal the degrees of freedom existing in the design of the compensator and can be utilized to solve the robust compensation problem. In order to reduce the effect of parameter uncertainties on the tracking error vector, the robust compensation problem is converted into a convex optimization problem with a set of linear matrix equation constraints. A simulation example is provided to illustrate the effectiveness of the proposed technique.

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

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