scholarly journals Admissible controls and controllable sets for a linear time-varying ordinary differential equation

2018 ◽  
Vol 8 (3) ◽  
pp. 1001-1019
Author(s):  
Lijuan Wang ◽  
◽  
Yashan Xu ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Linear Time ◽  
Time Varying ◽  
Admissible Controls

Existence of Solutions of Riccati Differential Equations

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Sinan Kilicaslan ◽  
Stephen P. Banks
Keyword(s):  
Differential Equation ◽  
Nonlinear Systems ◽  
Existence Of Solutions ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Time Varying ◽  
Riccati Differential Equation ◽  
Riccati Differential Equations ◽  
Time Varying Systems

A necessary condition for the existence of the solution of the Riccati differential equation for both linear, time varying systems and nonlinear systems is introduced. First, a necessary condition for the existence of the solution of the Riccati differential equation for linear, time varying systems is proposed. Then, the sufficient conditions to satisfy the necessary condition are given. After that, the existence of the solution of the Riccati differential equation is generalized for nonlinear systems.

ODE observers for DAE systems

2018 ◽  
Vol 36 (4) ◽  
pp. 1375-1393 ◽  
Author(s):  
Thomas Berger ◽  
Timo Reis
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Linear Time ◽  
Observer Design ◽  
Simple Criterion ◽  
Linear Time Invariant ◽  
Ode System ◽  
Dae Systems ◽  
Invariant Differential ◽  
Time Invariant

Abstract We consider linear time-invariant differential-algebraic systems which are not necessarily regular. The following question is addressed: when does an (asymptotic) observer which is realized by an ordinary differential equation (ODE) system exist? In our main result we characterize the existence of such observers by means of a simple criterion on the system matrices. To be specific, we show that an ODE observer exists if, and only if, the completely controllable part of the system is impulse observable. Extending the observer design from earlier works we provide a procedure for the construction of (asymptotic) ODE observers.

scholarly journals A Dynamic Scaling Law for Solar and Stellar Flare Loops

1989 ◽  
Vol 104 (2) ◽  
pp. 353-355
Author(s):  
George H. Fisher ◽  
Suzanne L. Hawley
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Heating Rate ◽  
Coronal Loop ◽  
Scaling Law ◽  
Dynamic Scaling ◽  
Time Varying ◽  
Stellar Flare ◽  
Flare Loops

AbstractWe discuss an ordinary differential equation which describes how the pressure in a coronal loop may evolve in time under the influence of a uniform, but time varying heating rate.

scholarly journals Exponential Stabilization of Linear Time-Varying Differential Equations with Uncertain Coefficients by Linear Stationary Feedback

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 853
Author(s):  
Vasilii Zaitsev ◽  
Inna Kim
Keyword(s):  
Differential Equation ◽  
Decay Rate ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Time Varying ◽  
Static State ◽  
Linear Time Invariant ◽  
Linear Differential ◽  
Time Invariant

We consider a control system defined by a linear time-varying differential equation of n-th order with uncertain bounded coefficients. The problem of exponential stabilization of the system with an arbitrary given decay rate by linear static state or output feedback with constant gain coefficients is studied. We prove that every system is exponentially stabilizable with any pregiven decay rate by linear time-invariant static state feedback. The proof is based on the Levin’s theorem on sufficient conditions for absolute non-oscillatory stability of solutions to a linear differential equation. We obtain sufficient conditions of exponential stabilization with any pregiven decay rate for a linear differential equation with uncertain bounded coefficients by linear time-invariant static output feedback. Illustrative examples are considered.

scholarly journals Inverse Commutativity Conditions for Second-Order Linear Time-Varying Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Mehmet Emir Koksal
Keyword(s):  
Differential Equation ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Time Varying ◽  
Order Linear ◽  
Time Varying Systems ◽  
Initial States ◽  
Necessary And Sufficient

The necessary and sufficient conditions where a second-order linear time-varying system A is commutative with another system B of the same type have been given in the literature for both zero initial states and nonzero initial states. These conditions are mainly expressed in terms of the coefficients of the differential equation describing system A. In this contribution, the inverse conditions expressed in terms of the coefficients of the differential equation describing system B have been derived and shown to be of the same form of the original equations appearing in the literature.

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