Realizations of linear control systems on time scales. (English) Zbl 1133.93033

Summary: Linear constant-coefficients control systems with output on arbitrary time scales are studied. Kalman criteria of controllability and observability are extended to such systems. The main problem is to find criteria for an abstract input/output map to have a realization as a system on the time scale. Two different characterizations of realizability are proved. They extend the classical results obtained for continuous-time and discrete-time systems. Minimal realizations and their uniqueness are also studied.


93C70 Time-scale analysis and singular perturbations in control/observation systems
93C05 Linear systems in control theory
93B05 Controllability
93B07 Observability
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