Temporal stabilizability and compensatability of time-varying linear discrete-time systems with white stochastic parameters

This paper reveals that apart from changes of system structure vital system properties such as stabilizability and compensatability may be lost temporarily due to the stochastic nature of system parameters. To that end new system properties called temporal mean-square stabilizability (tms-stabilizability) and temporal mean-square compensatability (tms-compensatability) for time-varying linear discrete-time systems with white stochastic parameters (multiplicative white noise) are developed. When controlling such systems by means of (optimal) state feedback, tms-stabilizability identifies intervals where mean-square stability (ms-stability) is lost temporarily. This is vital knowledge to both control engineers and system scientists. Similarly, tms-compensatability identifies intervals where ms-stability is lost temporarily in case of full-order (optimal) output feedback. Tests explicit in the system matrices are provided to determine each temporal system property. These tests compute measures of the associated temporal system properties. Relations among the new system properties as well as relations with associated existing system properties are investigated and established. Examples illustrating principal applications and practical importance are provided.