The problem of asymptotic tracking of reference signals is considered in the context of m-input, m-output linear systems (A, B, C) with the following structural properties: (i) CB is sign definite ( but not necessarily symmetric), (ii) the zero dynamics are exponentially stable. The class Y-ref(alpha) of reference signals is the set of all possible solutions of a fixed, stable, linear, homogeneous differential equation ( with associated characteristic polynomial alpha). The first control objective is asymptotic tracking, by the system output y = Cx, of any reference signal r is an element of Y-ref(alpha). The second objective is guaranteed error e = y - r transient performance: e should evolve within a prescribed performance funnel F-phi ( determined by a function phi). Both objectives are achieved simultaneously by an internal model in series with a proportional time-varying error feedback t bar right arrow u(t) = nu(k(t))e(t), where nu is a smooth function with the properties lim sup(k-->infinity) nu(k) = +infinity and lim inf(k-->infinity)nu(k) = -infinity, and k( t) is generated via a nonlinear function of the product parallel to e(t)parallel to phi(t). The feedback structure essentially exploits an intrinsic high-gain property of the system by ensuring that, if (t, e(t)) approaches the funnel boundary, then the gain attains values sufficiently large to preclude boundary contact.
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