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The stabilization with a General Dissipativity Constraint (GDC) has been governed by the non-negativeness of ΔV(x, k) along the trajectories (i.e. ΔV(x, k) 0), in which ΔV(x, k) 0 is a storage function. We have stated and proved the state convergence with the GDC a previous work, but the stability has not been addressed thoroughly. In this paper, we analyze the stability that is obtained from...
The main objective of this paper is to revisit one of the key steps of immersion and invariance stabilizing controller design. Namely, the one that ensures attractivity of the manifold whose internal dynamics contains a copy of the desired system behavior. Towards this end we invoke contraction theory principles and propose two alternative procedures to carry out this step: (i) to replace attractivity...
We consider control systems of the type x?? = Ax+??(t)ub, where u ?? R, (A; b) is a controllable pair and ?? is an unknown time-varying signal with values in [0; 1] satisfying a permanent excitation condition of the kind ??t+Tt ?? ?? ??for 0 < ?? ?? T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T; ??) if the real part of the...
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