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Estimates for perturbations of discounted Markov chains on general spaces

Raúl Montes-de-Oca, Alexander Sakhanenko, Francisco Salem-Silva (2003)

Applicationes Mathematicae

We analyse a Markov chain and perturbations of the transition probability and the one-step cost function (possibly unbounded) defined on it. Under certain conditions, of Lyapunov and Harris type, we obtain new estimates of the effects of such perturbations via an index of perturbations, defined as the difference of the total expected discounted costs between the original Markov chain and the perturbed one. We provide an example which illustrates our analysis.

Event-triggered H ∞ static output feedback control of discrete time piecewise-affine systems

Zhuyun Xue, Mouquan Shen (2021)

Kybernetika

This paper is concerned with the problem of H ∞ event-triggered output feedback control of discrete time piecewise-affine systems. Relying on system outputs, a piecewise-affine triggering condition is constructed to release communication burden. Resorting to piecewise Lyapunov functional and robust control techniques, sufficient conditions are built to ensure the closed-loop systems to be asymptotically stable with the prescribed H ∞ performance. By utilizing a separation strategy, the static output...

Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems

Cheng-Zhong Xu, Gauthier Sallet (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is...

Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems

Cheng-Zhong Xu, Gauthier Sallet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system...

Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics

Pascal Morin, Claude Samson (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Exponential stabilization of nonlinear driftless affine control systems is addressed with the concern of achieving robustness with respect to imperfect knowledge of the system's control vector fields. In order to satisfy this robustness requirement, and inspired by Bennani and Rouchon [1] where the same issue was first addressed, we consider a control strategy which consists in applying periodically updated open-loop controls that are continuous with respect to state initial conditions. These...

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