scholarly journals SUFFICIENT CONDITIONS FOR ROBUST OBSERVABILITY OF DISCRETE LINEAR TIME-VARYING SYSTEMS

2005 ◽  
Vol 38 (1) ◽  
pp. 215-220
Author(s):  
Jaewon Seo ◽  
Dohyoung Chung ◽  
Chan Gook Park ◽  
Jang Gyu Lee
Keyword(s):  
Linear Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Time Varying Systems

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.

Necessary and Sufficient Conditions for Assignability of the Lyapunov Spectrum of Discrete Linear Time-Varying Systems

2018 ◽  
Vol 63 (11) ◽  
pp. 3825-3837 ◽  
Author(s):  
Artur Babiarz ◽  
Irina Banshchikova ◽  
Adam Czornik ◽  
Evgenii K. Makarov ◽  
Michal Niezabitowski ◽  
...  
Keyword(s):  
Linear Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lyapunov Spectrum ◽  
Time Varying ◽  
Time Varying Systems ◽  
Necessary And Sufficient

scholarly journals Commutativity of Linear Time-Varying Differential Systems with Nonzero Initial Conditions: A Review and Some New Extensions

2011 ◽  
Vol 2011 ◽  
pp. 1-25 ◽  
Author(s):  
Muhammet Koksal ◽  
Mehmet Emir Koksal
Keyword(s):  
Initial Conditions ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Industrial Applications ◽  
Time Varying ◽  
Differential Systems ◽  
System Sensitivity ◽  
Time Varying Systems ◽  
A Chain ◽  
Fifth Order

Necessary and sufficient conditions for the commutativity of linear time-varying systems are derived in the case of nonzero initial conditions. It is shown that some commutative class of linear time-varying systems may not commute with arbitrary initial conditions. In this respect, commutativity of Euler differential systems is investigated. Explicit commutativity conditions for the fifth-order systems are solved. New results about the effects of commutativity on system sensitivity and disturbance properties are presented, which is very important for network design and industrial applications where many of the systems are composed of subsystems cooperating one after another in a chain. The results are supported by examples treated either analytically or numerically.

scholarly journals On the Uniform Exponential Stability of Time-Varying Systems Subject to Discrete Time-Varying Delays and Nonlinear Delayed Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Maher Hammami ◽  
Mohamed Ali Hammami ◽  
Manuel De la Sen
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Global Asymptotic Stability ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Uniform Exponential Stability ◽  
Time Varying Systems ◽  
Delayed Time

This paper addresses the problem of stability analysis of systems with delayed time-varying perturbations. Some sufficient conditions for a class of linear time-varying systems with nonlinear delayed perturbations are derived by using an improved Lyapunov-Krasovskii functional. The uniform global asymptotic stability of the solutions is obtained in terms of convergence toward a neighborhood of the origin.

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