Stability and Controls Analysis for Delay Systems

✍ Scribed by Jinrong Wang, Michal Feckan, Mengmeng Li

• Publisher: Academic Press
• Year: 2022
• Tongue: English
• Leaves: 332
• Category: Library

✦ Synopsis

Stability and Controls Analysis for Delay Systems is devoted to stability, controllability and iterative learning control (ILC) to delay systems, including first order system, oscillating systems, impulsive systems, fractional systems, difference systems and stochastic systems raised from physics, biology, population dynamics, ecology and economics, currently not presented in other books on conventional fields. Delayed exponential matrix function approach is widely used to derive the representation and stability of the solutions and the controllability. ILC design are also established, which can be regarded as a way to find the control function.

The broad variety of achieved results with rigorous proofs and many numerical examples make this book unique.

✦ Table of Contents

Front Cover
Stability and Controls Analysis for Delay Systems
Copyright
Contents
Preface
Acknowledgments
1 Introduction
2 Delay systems
2.1 Finite time stability
2.1.1 Finite time stability for linear delay differential systems
2.1.1.1 Finite time stability results based on Definition 2.1
2.1.1.2 Finite time stability results based on Definition 2.2
2.1.1.3 Numerical examples and discussion
2.1.1.4 Conclusion
2.1.2 Finite time stability for semilinear delay differential systems
2.1.2.1 Finite time stability results for system (2.25)
2.1.2.2 Finite time stability results for system (2.26)
2.1.2.3 Numerical examples and discussion
2.1.2.4 Conclusion
2.2 Controllability
2.2.1 Relative controllability for delay differential systems
2.2.1.1 Relative controllability for linear delay differential systems
2.2.1.2 Relative controllability for semilinear delay differential systems
2.2.1.3 Numerical examples and discussion
2.2.1.4 Conclusions
2.3 Iterative learning control
2.3.1 Iterative learning control for delay differential systems
2.3.1.1 Convergence analysis of P-type
2.3.1.2 Convergence analysis of D-type
2.3.1.3 Numerical examples and discussion
2.3.1.4 Conclusions
3 Oscillating delay systems
3.1 Finite time stability
3.1.1 Finite time stability of oscillating delay systems
3.1.1.1 Finite time stability results for linear systems
3.1.1.2 Extension to delay systems with nonlinear term
3.1.1.3 Numerical examples and discussion
3.1.1.4 Conclusion
3.2 Controllability
3.2.1 Controllability of delay oscillating systems
3.2.1.1 Controllability of linear delay systems
3.2.1.2 Controllability of nonlinear systems
3.2.1.3 Numerical examples and discussion
3.2.1.4 Conclusion
3.3 Iterative learning control
3.3.1 Iterative learning control for an oscillating system
3.3.1.1 Convergence analysis of P-type ILC
3.3.1.2 Convergence analysis of D-type ILC
3.3.1.3 Numerical examples and discussion
3.3.1.4 Conclusion
4 Impulsive delay systems
4.1 Asymptotical stability
4.1.1 Basic estimation and Gronwall-type inequalities
4.1.2 Linear impulsive delay differential systems
4.1.2.1 Impulsive delayed Cauchy matrix and its properties
4.1.2.2 Representation of solutions
4.1.2.3 Asymptotical stability results
4.1.2.4 Examples
4.1.2.5 Conclusion
4.2 Finite time stability
4.2.1 Representation of solutions
4.2.2 Finite time stability results
4.2.2.1 Impulsive condition (I1) holds
4.2.2.2 Impulsive condition (I2) holds
4.2.2.3 Numerical examples and discussion
4.2.2.4 Conclusion
4.3 Controllability
4.3.1 Controllability of impulsive delay differential systems
4.3.1.1 Relative controllability of linear systems
4.3.1.2 Relative controllability of semilinear systems
4.3.1.3 Numerical examples and discussion
4.3.1.4 Conclusion
5 Fractional delay systems
5.1 Finite time stability and controllability for Caputo type
5.1.1 Finite time stability for Caputo type
5.1.1.1 Representation of solutions for linear systems
5.1.1.2 Existence of solutions for nonlinear system
5.1.1.3 Finite time stability results for Caputo type
5.1.1.4 Numerical examples and discussion
5.1.1.5 Conclusion
5.1.2 Relative controllability results for Caputo type
5.1.2.1 Relative controllability results for linear systems
5.1.2.2 Relative controllability results for semilinear systems
5.1.2.3 Numerical examples and discussion
5.1.2.4 Conclusion
5.2 Finite time stability and controllability for Riemann–Liouville type
5.2.1 Finite time stability for Riemann–Liouville type
5.2.1.1 Representation of solutions for linear systems
5.2.1.2 Finite time stability for linear systems
5.2.1.3 Numerical example and discussion
5.2.1.4 Conclusions
5.2.2 Relative controllability for Riemann–Liouville type
5.2.2.1 Relative controllability for linear systems
5.2.2.2 Numerical example and discussion
5.2.2.3 Conclusions
6 Difference delay systems
6.1 Controllability
6.1.1 Controllability for linear discrete delay systems
6.1.1.1 New control functions
6.1.1.2 Relative controllability
6.1.1.3 Numerical example and discussion
6.1.1.4 Conclusions
6.2 Iterative learning control for fixed trial lengths
6.2.1 Iterative learning control for linear systems
6.2.1.1 ILC design and convergence analysis
6.2.1.2 Numerical examples and discussion
6.2.1.3 Conclusion
6.3 Iterative learning control for varying trial lengths
6.3.1 Iterative learning control for linear discrete delay systems
6.3.1.1 Discrete matrix delayed exponential function
6.3.1.2 Randomly varying trial lengths
6.3.1.3 ILC design and convergence analysis
6.3.1.4 Numerical examples and discussion
6.3.1.5 Conclusion
7 Stochastic delay systems
7.1 Controllability for first order systems
7.1.1 Null controllability stochastic delay systems
7.1.1.1 Null controllability for linear systems
7.1.1.2 Null controllability for semilinear systems
7.1.1.3 Numerical example and discussion
7.1.1.4 Conclusion
7.2 Controllability for oscillating systems
7.2.1 Controllability of stochastic oscillating delay systems driven by the Rosenblatt distribution
7.2.1.1 Controllability of stochastic linear oscillating delay systems
7.2.1.2 Controllability of stochastic nonlinear oscillating delay systems
7.2.1.3 Numerical examples and discussion
7.2.1.4 Conclusions
References
Index
Back Cover