2. Continuous-time linear systems and the Laplace transform

2020 ◽  
pp. 21-38
Keyword(s):  
Laplace Transform ◽  
Linear Systems ◽  
Continuous Time ◽  
The Laplace Transform ◽  
Time Linear

scholarly journals Descriptor fractional linear systems with regular pencils

2013 ◽  
Vol 23 (2) ◽  
pp. 309-315 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Laplace Transform ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
The State ◽  
Transition Matrices ◽  
State Equations ◽  
Numerical Examples ◽  
The Laplace Transform ◽  
Time Linear

Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.

scholarly journals Fractional Positive Continuous-Time Linear Systems and Their Reachability

2008 ◽  
Vol 18 (2) ◽  
pp. 223-228 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Positive Systems ◽  
State Equations ◽  
Fractional Systems ◽  
New Class ◽  
The Laplace Transform ◽  
Necessary And Sufficient ◽  
Time Linear

Fractional Positive Continuous-Time Linear Systems and Their ReachabilityA new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.

State space solution of implicit fractional continuous time systems

2012 ◽  
Vol 15 (3) ◽  
Author(s):  
Djillali Bouagada ◽  
Paul Dooren
Keyword(s):  
Laplace Transform ◽  
Fractional Derivative ◽  
State Space ◽  
Caputo Fractional Derivative ◽  
Continuous Time ◽  
State Space Models ◽  
Continuous Time Systems ◽  
The Laplace Transform ◽  
Time Systems ◽  
Time Linear

AbstractIn this work we extend a result from the literature on fractional continuous-time linear systems to the case of implicit fractional continuous-time state space models, based on the Caputo fractional derivative. The solution of the problem is derived using the Laplace transform.

scholarly journals Design of regular positive and stable descriptor systems via state-feedbacks for descriptor continuous-time linear systems with singular pencils

2014 ◽  
Vol 24 (3) ◽  
pp. 289-297
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Special Form ◽  
The State ◽  
New Method ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Asymptotically Stable ◽  
Numerical Example ◽  
Time Linear

Abstract A new method is proposed of design of regular positive and asymptotically stable descriptor systems by the use of state-feedbacks for descriptor continuous-time linear systems with singular pencils. The method is based on the reduction of the descriptor system by elementary row and column operations to special form. A procedure for the design of the state-feedbacks gain matrix is presented and illustrated by a numerical example

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