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The Rantzer multipliers are known to preserve the positivity of certain aberrations of memoryless monotone positive nonlinearities. We show that if the nonlinearity input is constrained to be positive valued for all time instants, these multipliers are positivity preserving for a larger class of nonlinearities. As a result, it follows that the Rantzer multipliers are useful in reducing the conservatism inherent in the multiplier theoretic stability analysis of feedback systems featuring a larger class of nonlinearities than the one these multipliers were originally intended for, so long as the nonlinearity input is positive-valued for all time instants. [ABSTRACT FROM AUTHOR]

Abstract-A formal theoretical explanation of the model-mismatch instability problem associated with certain adaptive control design schemes is proposed, and a solution is provided. To address the model-mismatch problem, a primary task of adaptive control is formulated as finding an asymptotically optimal, stabilizing controller, given the feasibility of adaptive control problem. A class of data-driven cost functions called cost-detectable is introduced that detect evidence of instability without reference to prior plant models or plant assumptions. The problem of designing adaptive systems that are robustly immune to mismatch instability problems is thus placed in a setting of a standard optimization problem. We call the result safe adaptive control because it robustly achieves adaptive stabilization goals whenever feasible, without prior assumptions on the plant model and, hence, without the risk of model-mismatch instability. The result improves the robustness of previous results in hysteresis switching control, both for discrete and for continuously-parameterized candidate controller sets. Examples are provided. [ABSTRACT FROM AUTHOR]

For a special class of systems, it is shown that the existence of a common quadratic Lyapunov function (CQLF) is necessary and sufficient for the stability of an associated switched system under arbitrary switching. Furthermore, it is shown that the existence of a CQLF for N (N > 2) subsystems is equivalent to the existence of a CQLF for every pair of sub-systems. An algorithm is proposed to compute a CQLF for the subsystems, when it exists, using the left and right eigenvectors of a critical matrix obtained from a matrix pencil. [ABSTRACT FROM AUTHOR]