Finite settling time stabilisation of a family of discrete-time systems

The problem of finding a compensator C, that stabilises in the Finite Settling Time (FST) sense, a family of k distinct discrete time plants {P(, i— 1, ..., fc}, is referred to as Simultaneous FST Stabilisation Problem (S-FSTSP) and it is examined here. The general case of many input, many output plants is considered first and algebraic conditions for the existence of a S-FSTS controller are derived in terms of the properties of the plants family matrix. For the special case of single input many output (SIMO), and many input single output (MISO) plant families, testable necessary and sufficient conditions for solvability of S-SFTSP are derived and whenever a solution exists, the family of solutions is given. The nature of the results is algebraic, since they depend on the properties of a rational vector space associated with the family; however, the final conditions are expressed as standard linear algebra tests.