Feasibility of nonlinear and adaptive control methodologies in multivariable lineartime-invariant systems with state space realization {A;B;C} has apparently beenlimited by the standard strict passivity (or positive realness) conditions that implythat the product CB must be positive definite symmetric. More recently the symmetrycondition has been mitigated, requiring instead that the not necessarily symmetricmatrix CB be diagonalizable and with positive real eigenvalues. The mitigated conditionswere useful in proving pure stabilizability with Adaptive Controllers. However,the Model Tracking question has remained open and some counterexamples seemedto demonstrate divergence of standard model reference adaptive controllers when theregular passivity conditions are not fully satisfied. Therefore, this paper further extendsthe previous results, showing that the new passivity conditions do guaranteestability with adaptive model tracking. Examples show how the new conditions solvethe case of flexible structures with unknown parameters when perfect collocation isnot possible. Also, the so called counterexample become simple, well-behaved, examples.
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