A SUBSPACE MODEL IDENTIFICATION SOLUTION TO THE IDENTIFICATION OF MIXED CAUSAL, ANTI-CAUSAL LTI SYSTEMS

This paper describes the modification of the family of MOESP(1) subspa ce algorithms when identifying mixed causal and anti-causal systems. I t is assumed that these class of systems have a regular pencil zE - A, where E is possibly singular. The key numerical problem in solving th is identification problem is the separation of the extended observabil ity matrix of the causal part from that of the anti-causal part when a mixture of both is determined from the input-output data. For the gen eral mixed causal, anti-causal case, this requires a partial calculati on of the Kronecker canonical form of the pencil zE - A, where the pai r [A E] has been determined from the recorded input-output data. For t he descriptor case, that is, when E is nilpotent, this problem is solv ed without computing the Kronecker canonical form. All existing member s of the MOESP family applicable to causal, linear, time-invariant sys tems are generalized. This allows a broad scope of identification prob lems for mixed causal, anti-causal systems to be addressed.