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In their 2001 paper, Potzsche, Siegmund and Wirth gave necessary and sufficient conditions for an LTI system on a time scale to have exponentially stable solutions based on pole placement. We find simple conditions for the stability of mu-varying scalar dynamic equations on time scales which are stochastically generated. As a special case, we examine the region in the complex plane which will guarantee the exponential stability of solutions of LTI systems. Via a decay analysis, we show how the tendency of the solution to grow or decay at each time step is determined by the pole placement within the region of exponential stability1.
Date of Conference: 11-13 March 2012