On Strictly Positive Realness in not necessarily symmetric systems

摘要

The standard Strictly PositivernRealness (SPR) relations seem to suggest thatrna definite symmetry is needed inrnmultivariable linear time-invariant systemsrnwith state space realization {A, B, C}.rnSpecifically, the product CB must be positiverndefinite symmetric. Recent publications havernalso shown that minimum-phase systems withrnsuch a CB product can be made strictlyrnpositive real via constant output feedback.rnThis condition may imply that the use of thernimportant SPR property in adaptive controlrnand other nonlinear control methodologies isrnlimited to symmetric systems. This paperrnattempts to expand the SPR property and itsrnapplicability to not necessarily symmetricrnsystems, ending with an adaptive controlrnillustration.