Uniformly observable linear nonstationary systems with many outputs and their canonical forms (Q5926572)

Linear, finite-dimensional, continuous-time control systems with time-dependent coefficients and many outputs are considered. Using algebraic and differential geometric methods, necessary and sufficient conditions for uniform observability in a given finite time interval are formulated and proved. Complete invariants of the action of the group of linear transformations with smooth coefficients on the set of uniformly observable dynamical systems are calculated. Moreover, several remarks and comments concerning canonical forms of uniformly observable control systems are given. Finally, an example of constructing a canonical form is presented. The relationships to observability results given in the literature are also pointed out and discussed. Observability problems for linear control problems have been recently considered in the monograph [\textit{T. Kaczorek}, ``Linear control systems'', New York, John Wiley \& Sons, Vol. 1 (1992; Zbl 0784.93002) and Vol. 2 (1993; Zbl 0784.93003)].