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Adaptive model tracking with mitigated passivity conditions

Itzhak Barkana
Feasibility of nonlinear and adaptive control methodologies in multivariable linear time-invariant systems with state space realization fA;B;Cg has apparently been limited by the standard strict passivity (or positive realness) conditions that imply that the product CB must be positive definite symmetric. A recent paper has managed to mitigate the symmetry condition, requiring instead that the positive definite and not necessarily symmetric matrix CB be diagonalizable. Although the mitigated conditions were useful in proving pure stabilizability with Adaptive Controllers, the Model Tracking question has remained open. This paper further extends the previous results, showing that the new passivity conditions can be used to guarantee stability of the adaptive control system and asymptotically
perfect model tracking.
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