© The Institution of Engineering and Technology
In a past study the authors drew attention to the fact that timevarying discretetime linear systems may be temporarily uncontrollable and unreconstructable and that this is vital knowledge for both control engineers and system scientists. Describing and detecting the temporal loss of controllability and reconstructability requires considering discretetime systems with variable dimensions and the jstep, kstep Kalman decomposition. In this study for linear discretetime systems with variable dimensions measures of temporal and onestep stabilisability and detectability are developed. These measures indicate to what extent the temporal loss of controllability and reconstructability may lead to temporal instability of the closedloop system when designing a static state or dynamic output feedback controller. The measures are calculated by solving specific linear quadratic cheap control problems by means of standard linear quadratic control algorithms. The importance of our developments for control system design is illustrated by means of two numerical examples.
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