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In this work, a novel perspective is developed to investigate the property of controllability/observability of linear switched sampled-data systems under the non-equidistant sampling schedule. In this regard, two new notions are introduced as ϵ -controllability and ϵ -observability to create a feasible ground for controlling and observing linear switched sampled-data systems with any initial time chosen from outside of ϵ neighborhood of switching instants. The main motivation is to control and observe the given switched sampled-data system, which consists of a finite number of discrete-time sub-systems within each sub-system. Hence, the system requires a lower number of sampling times for ϵ -controllability and ϵ -observability compared to the original notions of controllability and observability in this context. Although the number of sampling times in a certain time interval increases whenever ϵ tends to zero, the number of sampling candidates required for ϵ -controllability and ϵ -observability becomes finite. Numerical experiments are performed on several continuous time switched linear systems, and ϵ -controllability and ϵ -observability of their corresponding switched sampled-data systems are derived for various ϵ values under constructed non-equidistant sampling patterns. • Notions of ϵ -controllability and ϵ -observability are introduced in switched systems. • Kalman rank condition provides the property of ϵ -controllability/ ϵ -observability. • ϵ -Controllability/ ϵ -Observability requires less number of sampling times. • Different kinds of industrial problems are investigated in this context. [ABSTRACT FROM AUTHOR]

In this paper, the authors consider the asymptotic synchronization of a linear dissipative system with multiple feedback dampings. They first show that under the observability of a scalar equation, Kalman's rank condition is sufficient for the uniqueness of solution to a complex system of elliptic equations with mixed observations. The authors then establish a general theory on the asymptotic stability and the asymptotic synchronization for the corresponding evolutional system subjected to mixed dampings of various natures. Some classic models are presented to illustrate the field of applications of the abstract theory. [ABSTRACT FROM AUTHOR]

We study semigroups generated by general fractional Ornstein–Uhlenbeck operators acting on L 2 (R n) . We characterize geometrically the partial Gevrey-type smoothing properties of these semigroups, and we sharply describe the blow-up of the associated seminorms for short times, generalizing the hypoelliptic and the quadratic cases. As a byproduct of this study, we establish partial subelliptic estimates enjoyed by fractional Ornstein–Uhlenbeck operators on the whole space by using interpolation theory. [ABSTRACT FROM AUTHOR]

The focus of this paper is the exact controllability of a system of N one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We give a Kalman condition (necessary and sufficient) and give a description of the attainable set. In general, this set is not optimal, but can be refined under certain conditions. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of internal controllability of a system of heat equations posed on a bounded domain with Dirichlet boundary conditions and perturbed with analytic non-local coupling terms. Each component of the system may be controlled in a different subdomain. Assuming that the unperturbed system is controllable-a property that has been recently characterized in terms of a Kalman-like rank condition-the authors give a necessary and sufficient condition for the controllability of the coupled system under the form of a unique continuation property for the corresponding elliptic eigenvalue system. The proof relies on a compactness-uniqueness argument, which is quite unusual in the context of parabolic systems, previously developed for scalar parabolic equations. The general result is illustrated by two simple examples. [ABSTRACT FROM AUTHOR]

The objective of this paper is to make, in a simple and rigorous way, some contributions to the notion of output controllability. We first examine, for general linear time-invariant systems, the notion of state to output controllability, introduced in the 60s by Bertram and Sarachik. More precisely, we extend the Hautus test, well-known in the case of state controllability, to state to output controllability, and propose a controllability Gramian matrix, allowing us to build a continuous control achieving a transfer with minimal energy. We also give two other notions of output controllability, namely output to output and globally output to output controllability. For each of these two other new notions, we give necessary and sufficient conditions, in terms of Kalman rank, Hautus test and Gramian matrices. [ABSTRACT FROM AUTHOR]

In this work, a novel perspective is developed to investigate the property of controllability/observability of linear switched sampled-data systems under the non-equidistant sampling schedule. In this regard, two new notions are introduced as ϵ-controllability and ϵ-observability to create a feasible ground for controlling and observing linear switched sampled-data systems with any initial time chosen from outside of ϵ neighborhood of switching instants. The main motivation is to control and observe the given switched sampled-data system, which consists of a finite number of discrete-time sub-systems within each sub-system. Hence, the system requires a lower number of sampling times for ϵ-controllability and ϵ-observability compared to the original notions of controllability and observability in this context. Although the number of sampling times in a certain time interval increases whenever ϵ tends to zero, the number of sampling candidates required for ϵ-controllability and ϵ-observability becomes finite. Numerical experiments are performed on several continuous time switched linear systems, and ϵ-controllability and ϵ-observability of their corresponding switched sampled-data systems are derived for various ϵ values under constructed non-equidistant sampling patterns., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 ISA. Published by Elsevier Ltd. All rights reserved.)

In this paper we consider the boundary null controllability of a system of n parabolic equations on domains of the form Ω = (0, π) x Ω2 with Ω2 a smooth domain of ℝN--1, N >1. When the control is exerted on {0} x ϖ2 with ϖ2 ⊂Ω2, we obtain a necessary and sufficient condition that completely characterizes the null controllability. This result is obtained through the Lebeau--Robbiano strategy and requires an upper bound of the cost of the one-dimensional boundary null control on (0, π). The latter is obtained using the moment method and it is shown to be bounded by CeC/T when T goes to 0+. [ABSTRACT FROM AUTHOR]

In this work, we study the null-controllability properties of linear parabolic systems with constant coefficients in the case where several controls are acting on different distributed subdomains and/or on the boundary. We prove a Kalman rank condition in the one-dimensional case. In the case where only distributed controls are considered, we also establish related results such as a Carleman estimate. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to prove the controllability to trajectories of a system of n one-dimensional parabolic equations when the control is exerted on a part of the boundary by means of m controls. We give a general Kalman condition (necessary and sufficient) and also present a construction and sharp estimates of a biorthogonal family in to . [Copyright &y& Elsevier]

We study fractional hypoelliptic Ornstein-Uhlenbeck operators acting on L 2 (R n) satisfying the Kalman rank condition. We prove that the semigroups generated by these operators enjoy Gevrey regularizing effects. Two byproducts are derived from this smoothing property. On the one hand, we prove the null-controllability in any positive time from thick control subsets of the associated parabolic equations posed on the whole space. On the other hand, by using interpolation theory, we get global L 2 subelliptic estimates for the these operators. [ABSTRACT FROM AUTHOR]