arXiv subjects

Paolo Mason

Publications and source records attributed to Paolo Mason.

At least 19 recordsLinked to original sources

arXiv2026

Finite-Time Stabilization of Linear Systems via Optimal Control

This paper presents an optimal control framework for achieving finite-time stabilization of linear systems. By introducing a suitably constructed integral cost function, we derive a new class of nonlinear controllers that guarantee finite-time stability through the application of the optimality principle. The relationship between the resulting optimal control law and the associated value function is analyzed, leading to the derivation of a Hamilton-Jacobi-Bellman (HJB) equation and the study of its regularity properties. Numerical simulations validate the theoretical findings and illustrate the effectiveness of the proposed method. Furthermore, a discussion on estimating the convergence time is provided.

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arXiv2025

Controllable Sequences of Minimal Length for Discrete-Time Switched Linear Control Systems

In this paper, we provide a novel characterization of the reachable set of discrete-time switched linear control systems and a Kalman-type criterion for controllability, assuming that the switching parameter can be used as a control parameter in addition to the actual control variable. For controllable switched linear control systems it turns out that there always exists a switching sequence such that the reachable set of the corresponding linear time-variant system covers the whole state space after a sufficiently large time. We provide estimates on the minimal time guaranteeing this property in terms of the state dimension, number of modes and rank of the control matrices, and show that such estimates are actually tight in some relevant cases.

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arXiv2025

A Berger-Wang formula for impulsive switched systems

This paper addresses a class of impulsive systems defined by a mix of continuous-time and discrete-time switched linear dynamics. We first analyze a related class of weighted discrete-time switched systems for which we establish a Berger--Wang-type result. An analogous result is then derived for impulsive systems and subsequently used to characterize their exponential stability through a spectral approach, thereby extending existing results in switched-systems theory.

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arXiv2025

Stability criteria for singularly perturbed impulsive linear switched systems

We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove that the stability or instability of these auxiliary systems directly determines that of the original system in the regime of small singular perturbation parameters.

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arXiv2024

On universal classes of Lyapunov functions for linear switched systems

In this paper we discuss the notion of universality for classes of candidate common Lyapunov functions of linear switched systems. On the one hand, we prove that a family of absolutely homogeneous functions is universal as soon as it approximates arbitrarily well every convex absolutely homogeneous function for the $C^0$ topology of the unit sphere. On the other hand, we prove several obstructions for a class to be universal, showing, in particular, that families of piecewise-polynomial continuous functions whose construction involves at most $l$ polynomials of degree at most $m$ (for given positive integers $l,m$) cannot be universal.

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arXiv2024

Feedback stabilization via a quantum projection filter

This paper considers a simplified model of open quantum systems undergoing imperfect measurements obtained via a projection filter approach. We use this approximate filter in the feedback stabilization problem specifically in the case of Quantum Non-Demolition (QND) measurements. The feedback design relies on the structure of the exponential family utilized for the projection process. We demonstrate that the introduced feedback guarantees exponential convergence of the original filter equation toward a predefined target state, corresponding to an eigenstate of the measurement operator.

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arXiv2023

Exact solution and projection filters for open quantum systems subject to imperfect measurements

In this paper, we consider an open quantum system undergoing imperfect and indirect measurement. For quantum non-demolition (QND) measurement, we show that the system evolves on an appropriately chosen manifold and we express the exact solution of the quantum filter equation in terms of the solution of a lower dimensional stochastic differential equation. In order to further reduce the dimension of the system under study, we consider the projection on the lower dimensional manifold originally introduced in [1] for the case of perfect measurements. An error analysis is performed to evaluate the precision of this approximate quantum filter, focusing on the case of QND measurement. Simulations suggest the efficiency of the proposed quantum projection filter, even in presence of a stabilizing feedback control which depends on the projection filter.

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arXiv2022

Upper and lower bounds for the maximal Lyapunov exponent of singularly perturbed linear switching systems

In this paper we consider the problem of determining the stability properties, and in particular assessing the exponential stability, of a singularly perturbed linear switching system. One of the challenges of this problem arises from the intricate interplay between the small parameter of singular perturbation and the rate of switching, as both tend to zero. Our approach consists in characterizing suitable auxiliary linear systems that provide lower and upper bounds for the asymptotics of the maximal Lyapunov exponent of the linear switching system as the parameter of the singular perturbation tends to zero.

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arXiv2020

Feedback exponential stabilization of GHZ states of multi-qubit systems

In this paper, we consider stochastic master equations describing the evolution of a multi-qubit system interacting with electromagnetic fields undergoing continuous-time measurements. By considering multiple z-type (Pauli z matrix on different qubits) and x-type (Pauli x matrix on all qubits) measurements and one control Hamiltonian, we provide general conditions on the feedback controller and the control Hamiltonian ensuring almost sure exponential convergence to a predetermined Greenberger-Horne-Zeilinger (GHZ) state, which is assumed to be a common eigenstate of the measurement operators. We provide explicit expressions of feedback controllers satisfying such conditions. We also consider the case of only z-type measurements and multiple control Hamiltonians, and we discuss asymptotic convergence towards a predetermined GHZ state. Finally, we demonstrate the effectiveness of our methodology for a three-qubit system through numerical simulations.

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arXiv2020

Robust feedback stabilization of N-level quantum spin systems

In this paper, we consider N-level quantum angular momentum systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose unawareness of the initial state and physical parameters, entailing the introduction of an additional state representing the estimated quantum state. The evolution of the quantum state and its estimation is described by a coupled stochastic master equation. Here, we study the asymptotic behavior of such a system in presence of a feedback controller. We provide sufficient conditions on the feedback controller and on the estimated parameters that guarantee exponential stabilization of the coupled stochastic system towards an eigenstate of the measurement operator. Furthermore, we estimate the corresponding rate of convergence. We also provide parametrized feedback laws satisfying such conditions. Our results show the robustness of the feedback stabilization strategy considered in [21] in case of imprecise initialization of the estimated state and with respect to the unknown physical parameters.

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arXiv2020

Worst Exponential Decay Rate for Degenerate Gradient flows subject to persistent excitation

In this paper we estimate the worst rate of exponential decay of degenerate gradient flows $\dot x = -S x$, issued from adaptive control theory. Under persistent excitation assumptions on the positive semi-definite matrix $S$, we provide upper bounds for this rate of decay consistent with previously known lower bounds and analogous stability results for more general classes of persistently excited signals. The strategy of proof consists in relating the worst decay rate to optimal control questions and studying in details their solutions. As a byproduct of our analysis, we also obtain estimates for the worst $L_2$-gain of the time-varying linear control systems $\dot x=-cc^\top x+u$, where the signal $c$ is persistently excited, thus solving an open problem posed by A. Rantzer in 1999.

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arXiv2020

On the robustness of stabilizing feedbacks for quantum spin-1/2 systems

In this paper, we consider stochastic master equations describing the evolution of quantum spin-1/2 systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose that the initial states and the exact values of the physical parameters are unknown. We prove that the feedback stabilization strategy considered in [16] is robust to these imperfections. This is shown by studying the asymptotic behavior of the coupled stochastic master equations describing the evolutions of the actual state and the estimated one under appropriate assumptions on the feedback controller. We provide sufficient conditions on the feedback controller and a valid domain of estimated parameters which ensure exponential stabilization of the coupled system. Furthermore, our results allow us to answer positively to [15,Conjecture 4.4] in the case of spin-1/2 systems with unknown initial states, even in presence of imprecisely known physical parameters.

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arXiv2020

Lyapunov characterization of uniform exponential stability for nonlinear infinite-dimensional systems

In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks to this generalization, we provide characterizations of the uniform (with respect to disturbances) local, semi-global, and global exponential stability, through the existence of coercive and non-coercive Lyapunov functionals. The importance of the obtained results is underlined through some applications concerning 1) exponential stability of nonlinear retarded systems with piecewise constant delays, 2) exponential stability preservation under sampling for semilinear control switching systems, and 3) the link between input-to-state stability and exponential stability of semilinear switching systems.

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arXiv2019

On estimation and feedback control of spin-1/2 systems with unknown initial states

In this paper, we consider stochastic master equations describing the evolutions of quantum systems interacting with electromagnetic fields undergoing continuous-time measurements. In particular, we study feedback control of quantum spin-1/2 systems in the case of unawareness of initial states and in presence of measurement imperfections. We prove that the fidelity between the actual quantum filter and its associated estimated filter converges to one under appropriate assumption on the feedback controller. This shows the asymptotic convergence of such filters. In addition, for spin-J systems, we discuss heuristically the asymptotic behavior of the actual quantum filter and its associated estimated filter and the possibility of exponentially stabilizing such systems towards an eigenvector of the measurement operator by an appropriate feedback.

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arXiv2019

On exponential stabilization of two-qubit systems

In this paper, we consider a two-qubit system undergoing continuous-time measurements. In presence of multiple channels, we provide sufficient conditions on the continuous feedback control law ensuring almost sure exponential convergence to a predetermined Bell state. This is obtained by applying stochastic tools, Lyapunov methods and geometric control tools. With one channel, we establish asymptotic convergence towards a predetermined Bell state. In both cases, we provide explicit expressions of feedback control laws satisfying the above-mentioned conditions. Finally, we demonstrate the effectiveness of our methodology through numerical simulations.

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arXiv2019

On exponential stabilization of N-level quantum angular momentum systems

In this paper, we consider the feedback stabilization problem for N-level quantum angular momentum systems undergoing continuous-time measurements. By using stochastic and geometric control tools, we provide sufficient conditions on the feedback control law ensuring almost sure exponential convergence to a predetermined eigenstate of the measurement operator. In order to achieve these results, we establish general features of quantum trajectories which are of interest by themselves. We illustrate the results by designing a class of feedback control laws satisfying the above-mentioned conditions and finally we demonstrate the effectiveness of our methodology through numerical simulations for three-level quantum angular momentum systems.

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arXiv2019

On Exponential Stabilization of Spin-1/2 Systems

In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound of the convergence rate. Based on stochastic Lyapunov techniques, we propose a parametrized measurement-based feedback which ensures exponential convergence toward the excited state. Moreover, we give a lower bound of the convergence rate for this case. Then, we discuss the effect of each parameter appeared in the control law in the convergence rate. Finally, we illustrate the efficiency of such feedback law through simulations.

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arXiv2016

On feedback stabilization of linear switched systems via switching signal control

Motivated by recent applications in control theory, we study the feedback stabilizability of switched systems, where one is allowed to chose the switching signal as a function of $x(t)$ in order to stabilize the system. We propose new algorithms and analyze several mathematical features of the problem which were unnoticed up to now, to our knowledge. We prove complexity results, (in-)equivalence between various notions of stabilizability, existence of Lyapunov functions, and provide a case study for a paradigmatic example introduced by Stanford and Urbano.

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