Lyapunov Stability Criteria for Randomly Sampled Systems

This study is concerned with the asymptotic behavior of systems in which random sampling occurs; they are studied by a stochastic Lyapunov function method. The control loops under consideration consist of a random sampler (a sampling device which closes at a set of statistically described times in lieu of periodic intervals), a zero order hold, a linear plant, and a feedback element. Sampled systems are modelled randomly when sampler imperfections such as jitter or skipping occur or when a single computer or communications link is a component of multiple control loops (that is, when the availability times of the computer or communications link to a particular control loop are random). This type of model has also been suggested for a human operator performing a compensatory tracking function. Improved stability criteria are given for systems whose inputs are identically zero for all time. When the feedback element is linear, sufficient conditions for asymptotic mean-square stability and asymptotic stability with probability one are obtained and compared. Necessary and sufficient conditions are also presented; these are used to analyze the value of the sufficient conditions. Intersample behavior is studied and results are presented for both stable and unstable plants. Numerical results illustrate the applicability and utility of the criteria presented and describe some interesting phenomena such as jitter stabilized systems. When random inputs are present, a general method is given for the computation of the asymptotic mean-square output at sample instants. This method is illustrated by a computer program for a general second-order system. A randomly sampled Lure problem is studied and sufficient conditions for asymptotic mean-square stability and asymptotic stability with probability one are derived. SUMMARY This study is concerned with the asymptotic behavior of systems in which random sampling occurs: they are studied by a stochastic Lyapunov function method. The control loops under consideration consist of a random sampler (a sampling device which closes at a set of statistically described times in lieu of periodic intervals), a zero order hold, a linear plant, and a feedback element. Sampled systems are modelled randomly when sampler imperfections, such as jitter or skipping, occur or when a single computer or communications link is a component of mul­ tiple control loops (that is, when the availability times of the computer or communications link to a particular control loop are random). This type of model has also been suggested for a human operator performing a compensatory …