A Necessary and Sufficient Condition for Stabilization of Switched Descriptor Time-Delay Systems Under Arbitrary Switching

2014 ◽  
Vol 18 (1) ◽  
pp. 266-272 ◽  
Author(s):  
Jiemei Zhao ◽  
Lijun Zhang ◽  
Xue Qi
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Necessary And Sufficient Condition ◽  
Arbitrary Switching ◽  
Necessary And Sufficient

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.

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.

On Stability Analysis of Switched Linear Time-Delay Systems under Arbitrary Switching

2015 ◽  
pp. 480-515 ◽  
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Lyapunov Function ◽  
Continuous Time ◽  
Delay System ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Delay Systems ◽  
Arbitrary Switching ◽  
The Stability

This chapter focuses on the stability analysis problem for a class of continuous-time switched time-delay systems modelled by delay differential equations under arbitrary switching. Then, a transformation under the arrow form is employed. Indeed, by using a constructed Lyapunov function, the aggregation techniques, the Kotelyanski lemma associated with the M-matrix properties, new delay-dependent sufficient stability conditions are derived. The obtained results provide a solution to one of the basic problems in continuous-time switched time-delay systems. This problem ensures asymptotic stability of the switched time-delay system under arbitrary switching signals. In addition, these stability conditions are extended to be generalized for switched systems with multiple delays. Noted that, these obtained results are explicit, simple to use, and allow us to avoid the problem of searching a common Lyapunov function. Finally, two examples are provided, with numerical simulations, to demonstrate the effectiveness of the proposed method.

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