In this work we study the filtering and optimal control problems for linear systems subject to abrupt changes in the parameters and partial observations. We assume that the abrupt changes are represented by independent and identically distributed random variables along the time, taking values in a finite set of numbers. Initially we present recursive filters of minimum mean square quadratic errors for this family of systems. These results generalize some previous results in the literature which only considered binary abrupt variations in the output variables of the system. Next we consider the quadratic optimal control problem for the partial observation case. Using the filter previously developed we present a sub-optimal solution for the problem, since that the separation principles cannot be applied to this case.
Recursive filters; abrupt variations; linear systems; quadratic control
