Minimality of Linear Switched Systems with known switching signal

Minimal realization is discussed for linear switched systems with a given switching signal. We propose consecutive forward and backward approach the time-interval of interest. The refers to extending reachable subspace at each time by taking into account nonzero space from previous mode. Afterwards, extends observable current mode observability information next account. This results in an overall reduced system which minimal has same input-output behavior as original system. Some examples are provided illustrate approach.