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This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust stability...
This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems including some constant delays and time-varying cone-bounded nonlinearities. Sufficient stability conditions are derived by taking into account the weighting factors describing the nonlinearities. The proposed results are applied to the stability analysis of a class of lossless transmission line models.
This note proposes a quite general mathematical proposition which can be a starting point to prove many well-known results encountered while studying the theory of linear systems through matrix inequalities, including the S-procedure, the projection lemma and few others. Moreover, the problem of robustness with respect to several parameter uncertainties is revisited owing to this new theorem, leading to LMI (Linear Matrix Inequality)-based conditions for robust stability or performance analysis...
A problem of inner convex approximation of a stability domain for continuous-time linear systems is addressed in the paper. A constructive procedure for generating stable cones in the polynomial coefficient space is explained. The main idea is based on a construction of so-called Routh stable line segments (half-lines) starting from a given stable point. These lines (Routh rays) represent edges of the corresponding Routh subcones that form (possibly after truncation) a polyhedral (truncated) Routh...
We study the dynamic behavior and stability of two connected
Rayleigh beams that are subject to, in addition to two sensors and
two actuators applied at the joint point, one of the actuators also
specially distributed along the beams. We show that with the
distributed control employed, there is a set of generalized
eigenfunctions of the closed-loop system, which forms a Riesz basis
with parenthesis for the state space. Then both the
spectrum-determined growth condition and exponential stability...
Let be a general control system; the existence of a smooth control-Lyapunov function does not imply the existence of a continuous stabilizing feedback. However, we show that it allows us to design a stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover, we recall a definition of a control-Lyapunov function in the case of a nonsmooth function; it is based on Clarke’s generalized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov...
Let be a general control system; the existence of a
smooth control-Lyapunov function does not imply the existence of a continuous
stabilizing feedback. However, we show that it allows us to design a
stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover,
we recall a definition of a control-Lyapunov function
in the case of a nonsmooth function; it is based on Clarke's
generalized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov...
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