Stability determination method for Metzler time-varying delay system

Abstract

The invention discloses a l1 small gain theorem and a stability determination method for an Metzler time-varying delay system based on the theorem. The stability determination method comprises the steps that a classical small gain theorem is extended based on a l1 stability concept to construct the l1small gain theorem, and a l1 stability sufficient condition for an M-delta feedback control systemis established; an Metzler dynamic system with time-varying delay is modeled, and a feedback control system composed of a deterministic system M and an uncertain system delta is constructed, a delay-dependent relevant portion of the Metzler time-varying delay system is regarded as a linear uncertainty operator; and based on the constructed l1 small gain theorem, a stability criterion of the Metzler time-varying delay system is established. This theorem can provide a powerful tool for a series of questions of the l1 stability in the field of analytical control, and can be used for the analysisand study of non-negative constrained dynamic systems with time-delay, such as in economics, population systems, biology, and networks.

Description

technical field [0001] The invention belongs to the technical field of time-delay system stability analysis, and specifically relates to a 1 Small gain theorem and based on l 1 Metzler's method for judging the stability of time-varying time-delay systems based on the small gain theorem. Background technique [0002] Lag is the range of time lag between the occurrence of an action and its effect. The time lag effect widely exists in all aspects of industrial production, data transmission, physical transportation, etc., and even in the financial, economic, social, and cultural environments, time lag is unavoidable. [0003] For example, in the financial market, the rise and fall of stocks are usually affected by multiple complex factors such as policy changes, economic environment, and major capital in and out. To put it simply, when the economic policy is favorable and the real economy environment is strong, a large amount of capital flows into the stock market, driving th...

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Problems solved by technology

However, the existence of time delays, especially time-varying time delays, introduces great difficulties to the study of Metzler time-delay systems

At present, the research on the stability of the Metzler time-delay system is very limited. The existing research mainly uses the classical robust control theory method to approximate the estimation by obtaining the structural singular value of the system. However, no matter from the perspective of analysis or calculation, , are more complex

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