Frequency-domain estimates of the sampling interval in multirate nonlinear systems by time-delay approach

ABSTRACT

A class of nonlinear hybrid systems consisting of a continuous plant and a multirate sampled-data controller is considered. Applying the time-delay approach, the system is transformed to the system with a time-varying sawtooth delay. Then, the value of the sampling intervals ensuring stability of the closed-loop system is estimated based on the frequency-domain circle-like criterion for systems with time-varying delay. Such a criterion for multirate MIMO systems is established based on the previous result for SISO systems proposed by M.Churilova in 1995. Efficiency and advantages of the method are illustrated by numerical examples. The key advantage of the proposed approach is that it is applicable to multirate systems nonaffine in control. It allows one to use a nonlinear feedback for stabilisation. Particularly, the case of nonsmooth or discontinuous nonlinear systems can be treated.

KEYWORDS:

• Stability of nonlinear systems
• hybrid systems
• Lyapunov function
• sampling intervals
• frequency domains
• multirate systems

Acknowledgments

The work was supported by the Government of Russian Federation [grant 074-U01] and by 111 Project No.D17019. The results for nonlinear system with a nonlinear sampled-data control (Section 3.1) were developed in IPME RAS under sole support of the Russian Science Foundation [grant 14-29-00142].

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Government of Russian Federation [grant 074-U01] and by 111 Project No.D17019. The results for nonlinear system with a nonlinear sampled-data control (Section 3.1) were developed in IPME RAS under sole support of the Russian Science Foundation [grant 14-29-00142