to the unmodified (ideal) reference system, discuss robustness of the proposed approach with respect to time-varying uncertainties and disturbances, and make connections to gradient minimization and classical control theory.

 

Notation
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The notation used in this paper is fairly standard. Specifically, $\IR$ denotes the set of real numbers, $\IR^n$ denotes the set of $n \times 1$ real column vectors, $\IR^{n \times m}$ denotes the set of $n \times m$ real matrices, $\IR_+$ (resp., $\overline{\IR}_+$) denotes the set of positive (resp., nonnegative-definite) real numbers, $\IR_+^{n \times n}$ (resp., $\overline{\IR}_+^{\hspace{0.1em} n \times n}$) denotes the set of $n \times n$ positive-definite (resp., nonnegative-definite) real matrices, $\IS^{n \times n}$ denotes the set of $n \times n$ symmetric real matrices, $\mathbb{D}^{n \times n}$ denotes the $n \times n$ real matrices with diagonal scalar entries, $(\cdot)\mT$ denotes transpose, $(\cdot)^{-1}$ denotes inverse, and “$\triangleq$” denotes equality by definition. In addition, we write $\lambda_{\rom{min}}(A)$ (resp., $\lambda_{\rom{max}}(A)$) for the minimum (resp., maximum) eigenvalue of the Hermitian matrix $A$, $\rom{tr}(\cdot)$ for the trace operator, $\rom{vec}(\cdot)$ for the column stacking operator, $\norm{\cdot}_2$ for the Euclidian norm, $\norm{\cdot}_\infty$ for the infinity norm, and $\norm{\cdot}_\rom{F}$ for the Frobenius matrix norm. Furthermore, for a signal $x(t)=[x_1(t), x_2(t), \ldots, x_n(t)]\mT \in \IR^n$ defined for 