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In contrast with traditional control input design techniques based on mathematical models of the system, in data-driven control approaches, which have recently gained substantial attention, the controller is derived directly from the data that are collected from experiments or observations of the target system. In particular, several data-driven optimal control and model predictive control (MPC) techniques have been proposed. In this paper, it is shown that the recently proposed data-driven LQR (Linear Quadratic Regulator) has a stability margin that is the set of the uncertainties in the control input channels maintaining the closed-loop stability. As an application of the proposed stability margin of the data-driven LQR, the consensus problem is considered. Since the control design for the consensus of multi-agent systems can be reformulated into the robust stabilization of a linear system with uncertainty in the input channel, it is demonstrated that the derived stability margin can be used to design a controller for the consensus of multi-agent systems. [ABSTRACT FROM AUTHOR]

Two new approaches to designing positive linear observers for positive linear systems are proposed. The first one employs a coordinates transformation and the second relies on the theory of positive realization. These approaches allow one to enlarge the class of positive systems that admit positive linear observers. New results on compartmental systems are also presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new framework of observer error linearization problem is proposed. The main idea of our approach is twofold. The one is to introduce an auxiliary dynamics whose input is the system output, and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics. It is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output. It is also shown that whenever an n dimensional system is immersible into an dimensional linear system up to an output injection, then it can be also dynamically observer error linearizable in our sense with a d dimensional auxiliary dynamics. Moreover, we show that the converse is not true by providing a counterexample, which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method. [Copyright &y& Elsevier]

Abstract: The class of nonlinear systems that can be put into nonlinear observer form (linear system with output injection) can be broadened if we employ the system immersion. We provide an immersion algorithm for SISO nonlinear systems with relative degree r. The proposed algorithm is an extension of the previous results and does not require the relative degree 1 assumption. In addition, it is seen that the immersion can always be computed via algebraic computations and simple integrations except in a very special case in which the relative degree equals the system dimension (in this case, only one first order differential equation appears in the algorithm). [Copyright &y& Elsevier]

There exists a class of non-linear systems which cannot be transformed into non-linear observer form via diffeomorphism, but can be immersed into higher dimensional non-linear observer form. This paper investigates when n dimensional non-linear systems can be immersed into ( n + m )-dimensional non-linear systems in non-linear observer form, and provides a necessary and sufficient condition. We also present an algorithm to check the immersibility. In general, at the first step of the algorithm, one should solve a differential equation with m + 1 unknowns rather than solving one with n + m unknowns simultaneously. When a solution to the differential equation can be obtained, the immersibility can be checked by a recursive algorithm. Moreover, when 2 m ≤ n , a straightforward algorithm is provided to check the immersibility. [ABSTRACT FROM AUTHOR]

Abstract: This study addresses the problem of consensus of multi-agent systems, consisting of a set of identical MIMO LTI systems, under a time-varying network that has a well-defined average (with uniform convergence to the average). The information delivered through the communication network is the output of each system. First, it is shown that consensus is reached asymptotically by using a group of compensators if the network switches sufficiently fast and the compensators are designed such that the multi-agent system asymptotically achieves consensus for the average of the network. Further, we find a relation between the two agreements, one obtained from considering the switching network and the other obtained from replacing the network with its average. Then, for a class of minimum phase systems, we remove the fast switching condition by redesigning the compensators. Finally, the formation stabilization of unicycle-type mobile robots is dealt with as an application of the problem, and it is demonstrated via a computer simulation. [Copyright &y& Elsevier]

Abstract: In this paper, we study the consensus (and synchronization) problem for multi-agent linear dynamic systems. All the agents have identical MIMO linear dynamics which can be of any order, and only the output information of each agents is delivered throughout the communication network. It is shown that consensus is reached if there exists a stable compensator which simultaneously stabilizes systems in a special form, where is the number of agents. We show that there exists such a compensator under a very general condition. Finally, the consensus value is characterized as a function of initial conditions with stable compensators in place. [Copyright &y& Elsevier]

Abstract: Some control problems in practice are often formulated as a linear output regulation problem with time-varying exosystems. Although this problem has been studied recently, an explicit and constructive solution has been given only for minimum phase systems. This paper presents a solution for non-minimum phase systems whose zero dynamics is hyperbolic (or has an exponentially dichotomic split in the case of time-varying zero dynamics). The idea is inspired by the non-causal stable inversion. [Copyright &y& Elsevier]