Output details

Strong stability of discrete-time systems

The paper extends the notion of “strong stability” to discrete-time, autonomous system descriptions. Three refined notions of strong stability are introduced and necessary and sufficient conditions for each of them are derived. Links between eigenframe-skewness and the violation of strong stability property are derived, which is potentially important for establishing links between Control Theory and Numerical Linear Algebra. Since eigenvalue sensitivity typically increases with large deviations of the matrix from normality, these links have important implications for robust control-system design. Closed-form solutions are finally obtained to the general discrete-time strong stabilisation problem under state and output feedback.