Necessary and sufficient condition for finite horizon H∞ estimation of time delay systems

2004 ◽  
Author(s):  
Huanshui Zhang ◽  
D. Zhan ◽  
Lihua Xie
Keyword(s):  
Time Delay ◽  
Finite Horizon ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Estimation Of Time

scholarly journals Reachable Set Bounding for Homogeneous Nonlinear Systems with Delay and Disturbance

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Xingao Zhu ◽  
Yuangong Sun
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Nonlinear Systems ◽  
Reachable Set ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Positive Systems ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

Reachable set bounding for homogeneous nonlinear systems with delay and disturbance is studied. By the usage of a new method for stability analysis of positive systems, an explicit necessary and sufficient condition is first derived to guarantee that all the states of positive homogeneous time-delay systems with degree p>1 converge asymptotically within a specific ball. Furthermore, the main result is extended to a class of nonlinear time variant systems. A numerical example is given to demonstrate the effectiveness of the obtained results.

Finite-horizon optimal control of unknown nonlinear time-delay systems

2017 ◽  
Vol 238 ◽  
pp. 277-285 ◽  
Author(s):  
Xiaohong Cui ◽  
Huaguang Zhang ◽  
Yanhong Luo ◽  
He Jiang
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Finite Horizon ◽  
Delay Systems ◽  
Time Delay Systems

Discretized Lyapunov-Krasovskii Functional for Systems With Multiple Delay Channels

2008 ◽  
Author(s):  
Hongfei Li ◽  
Keqin Gu
Keyword(s):  
Time Delay ◽  
Standard Form ◽  
Computational Effort ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
State Variables ◽  
Regular Time ◽  
Low Dimensional ◽  
Necessary And Sufficient

Many practical systems have a large number of state variables but only a few components have time delays. These delay components are often scalar or low dimensional, and involve single time delay in each component. A coupled differential-difference equation is well suited to formulate such systems. It is known that such a formulation is very general. Systems with multiple related or independent delays can be transformed into this standard form. Similar to regular time-delay systems, the existence of a quadratic Lyapunov-Krasovkii functional is necessary and sufficient for stability. This article discusses the discretization of such a quadratic Lyapunov-Krasovskii functional. Even for time-delay systems of retarded type, the formulation has significant advantage over the traditional formulation, as the size of the resulting linear matrix inequalities are drastically reduced for such systems. Indeed, the computational effort needed for checking stability of such a large system with a few low dimensional delays is quite reasonable.

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