122 research outputs found
Robustness of controllers designed using Galerkin type approximations
One of the difficulties in designing controllers for infinite-dimensional systems arises from attempting to calculate a state for the system. It is shown that Galerkin type approximations can be used to design controllers which will perform as designed when implemented on the original infinite-dimensional system. No assumptions, other than those typically employed in numerical analysis, are made on the approximating scheme
Exponential stabilization of infinite-dimensional systems by finite-dimensional controllers
This paper studies the feedback stabilization of abstract Cauchy problems
with unbounded output operators by finite-dimensional controllers. Both
necessary conditions and sufficient conditions for feedback stabilizability are
presented. The proof of closed-loop stability is based on a novel input-output
gain introduced in this paper. For systems satisfying a property we call
quasi-finite, an equivalent characterization of feedback stabilizability is
obtained. Quasi-finiteness is verified for classes of parabolic and hyperbolic
equations
About Robust Stability of Dynamic Systems with Time Delays through Fixed Point Theory
This paper investigates the global asymptotic stability independent of the sizes of the delays of linear time-varying systems with internal point delays which possess a limiting equation via fixed point theory. The error equation between the solutions of the limiting equation and that of the current one is considered as a perturbation equation in the fixed- point and stability analyses. The existence of a unique fixed point which is later proved to be an asymptotically stable equilibrium point is investigated. The stability conditions are basically concerned with the matrix measure of the delay-free matrix of dynamics to be negative and to have a modulus larger than the contribution of the error dynamics with respect to the limiting one. Alternative conditions are obtained concerned with the matrix dynamics for zero delay to be negative and to have a modulus larger than an appropriate contributions of the error dynamics of the current dynamics with respect to the limiting one. Since global stability is guaranteed under some deviation of the current solution related to the limiting one, which is considered as nominal, the stability is robust against such errors for certain tolerance margins.</p
Stabilizability of Markov jump linear systems modeling wireless networked control scenarios (extended version)
The communication channels used to convey information between the components
of wireless networked control systems (WNCSs) are subject to packet losses due
to time-varying fading and interference. The WNCSs with missing packets can be
modeled as Markov jump linear systems with one time-step delayed mode
observations. While the problem of the optimal linear quadratic regulation for
such systems has been already solved, we derive the necessary and sufficient
conditions for stabilizability. We also show, with an example considering a
communication channel model based on WirelessHART (a on-the-market wireless
communication standard specifically designed for process automation), that such
conditions are essential to the analysis of WNCSs where packet losses are
modeled with Bernoulli random variables representing the expected value of the
real random process governing the channel.Comment: Extended version of the paper accepted for the presentation at the
58th IEEE Conference on Decision and Control (CDC 2019
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