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.

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.

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

scholarly journals Novel Stability Criteria of Nonlinear Uncertain Systems with Time-Varying Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Yali Dong ◽  
Shengwei Mei ◽  
Xueli Wang
Keyword(s):  
Nonlinear Systems ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Riccati Differential Equations ◽  
Continuous State ◽  
Varying Delay

The problem of robust exponential stabilization for dynamical nonlinear systems with uncertainties and time-varying delay is considered in the paper. By constructing the proposed Lyapunov-Krasovskii functional approach, continuous state feedback controllers are put forward, and the criteria which guarantee the exponential stabilization of the nonlinear systems with uncertainties and time-varying delay are established in terms of solutions to the standard Riccati differential equations. Furthermore, based on the Lyapunov method and the linear matrix inequality approach, the sufficient conditions of exponential stability for a class of uncertain systems with time-varying delays and nonlinear perturbations are derived. Finally, two numerical examples are given to demonstrate the validity of the results.

scholarly journals Practical partial stability of time-varying systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Abdelfettah Hamzaoui ◽  
Nizar Hadj Taieb ◽  
Mohamed Ali Hammami
Keyword(s):  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Converse Theorem ◽  
Partial Stability ◽  
Perturbed Systems ◽  
Time Varying Systems ◽  
Made In

<p style='text-indent:20px;'>In this paper we investigate the practical asymptotic and exponential partial stability of time-varying nonlinear systems. We derive some sufficient conditions that guarantee practical partial stability of perturbed systems using Lyapunov's theory where a converse theorem is presented. Therefore, we generalize some works which are already made in the literature. Furthermore, we present some illustrative examples to verify the effectiveness of the proposed methods.</p>

Sign in / Sign up

Export Citation Format

Share Document