This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of systems (among them converse Lyapunov results). The proposed framework can allow the study of discontinuous solutions for nonlinear systems described by a single first-order hyperbolic partial differential equation under the effect of measurable inputs acting on...
For a general time-varying system, we prove that existence of an “Output Robust Control Lyapunov Function” implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the resulting closed-loop system. The main results of the present work constitute generalizations of a well known result due to Coron and Rosier [J. Math. Syst. Estim. Control 4 (1994) 67–84] concerning stabilization of autonomous systems by means of time-varying periodic...
For a general time-varying system, we prove that existence of an “Output
Robust Control Lyapunov Function” implies existence of continuous
time-varying feedback stabilizer, which guarantees output asymptotic
stability with respect to the resulting closed-loop system. The main results
of the present work constitute generalizations of a well known result
due to Coron and Rosier [
(1994) 67–84] concerning
stabilization of autonomous systems by means of time-varying periodic
feedback.
...
In this work, we propose a methodology for the expression of necessary and
sufficient Lyapunov-like conditions for the existence of stabilizing
feedback laws. The methodology is an extension of the well-known Control
Lyapunov Function (CLF) method and can be applied to very general nonlinear
time-varying systems with disturbance and control inputs, including both
finite and infinite-dimensional systems. The generality of the proposed
methodology is also reflected upon by the fact that partial...
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