论文信息 - Computing maximum delay deviation allowed to retain stability in systems with two delays

Computing maximum delay deviation allowed to retain stability in systems with two delays

This chapter discusses the calculation of maximum delay deviation without losing stability for systems with two delays. This work is based on our previous work on the properties of the stability crossing curves in the delay parameter space. Based on the results, an algorithm to calculate the maximum radius of delay deviation without changing the number of right hand zeros of the characteristic quasipolynomial can be devised. If the nominal system is stable, then the system remains stable when the delays do not deviate more than this radius.

[1] S. Lunel,et al. Delay Equations. Functional-, Complex-, and Nonlinear Analysis , 1995 .

[2] V. Kolmanovskii,et al. Stability of Functional Differential Equations , 1986 .

[3] G. Stépán. Retarded dynamical systems : stability and characteristic functions , 1989 .

[4] K. Cooke,et al. Discrete delay, distributed delay and stability switches , 1982 .

[5] Francis C. Moon,et al. Dynamics and chaos in manufacturing processes , 1998 .

[6] John L. Casti,et al. Introduction to the theory and application of differential equations with deviating arguments , 1973 .

[7] Jie Chen,et al. On stability crossing curves for general systems with two delays , 2004 .

[8] Jack K. Hale,et al. Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[9] J. Hale,et al. Global geometry of the stable regions for two delay differential equations , 1993 .

[10] Vladimir L. Kharitonov,et al. Stability of Time-Delay Systems , 2003, Control Engineering.

[11] S. Niculescu. Delay Effects on Stability: A Robust Control Approach , 2001 .

[12] Henryk Górecki,et al. Analysis and Synthesis of Time Delay Systems , 1989 .