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In this paper we study the question under which conditions a linear multi-modal system is disturbance decoupled. We establish necessary and sufficient geometric conditions from which the existing results on switched linear systems and conewise linear systems can be recovered as special cases. Also, we apply these conditions to a class of linear complementarity systems in order to obtain a more crisp characterization.

This paper deals with robust synchronization of directed and undirected multi-agent networks with uncertain agent dynamics. Given a network with identical nominal dynamics, we allow uncertainty in the form of coprime factor perturbations of the transfer matrix of the agent dynamics. These perturbations are assumed to be stable and have H-infinity-norm that is bounded by an a priori given desired tolerance. We derive state space equations for dynamic observer based protocols that achieve robust synchronization in the presence of such uncertainty. We obtain an achievable interval, i.e. an interval such that for each value of the tolerance contained in this interval there exists a robustly synchronizing protocol. (C) 2016 Elsevier B.V. All rights reserved.

This paper deals with model reduction by balanced truncation of switched linear systems (SLS). We consider switched linear systems whose dynamics, depending on the switching signal, switches between finitely many linear systems with a common state space. These linear systems are called the modes of the SLS. The idea is to seek for conditions under which there exists a single state space transformation that brings all modes of the SLS in balanced coordinates. As a measure of reachability and observability of the state components of the SLS, we take the average of the diagonal gramians. We then perform balanced truncation by discarding the state components corresponding to the smallest diagonal elements of this average balanced gramian. In order to carry out this program, we derive necessary and sufficient conditions under which a finite collection of linear systems with common state space can be balanced by a single state space transformation. Among other things, we derive sufficient conditions under which global uniform exponential stability of the SLS is preserved under simultaneous balanced truncation. Likewise, we derive conditions for preservation of positive realness or bounded realness of the SLS. Finally, in case that the conditions for simultaneous balancing do not hold, or we simply do not want to check these conditions, we propose to compute a suitable state space transformation on the basis of minimization of an overall cost function associated with the modes of the SLS. We show that in case our conditions do hold, this transformation is in fact simultaneously balancing, bringing us back to the original method described in this paper. IEEE Control Systems Society

Lately, with the increasing use of automated manual transmissions (AMT) the engagement control of the dry clutch becomes more important. The engagement control plays a crucial role, since different and conflicting objectives have to be satisfied: preservation of driver comfort, fast engagement and small friction losses. In this paper two optimal control strategies for clutch engagement, based on hybrid control principles, are compared. For developing a useful clutch control scheme, the driveline is modelled as a piecewise linear system. The first control strategy is widely known as explicit MPC. However, it seems that it is not suitable (yet) for this type of problem. The second strategy is a piecewise LQ controller, based on piecewise quadratic Lyapunov functions. Simulation results obtained with both strategies are presented and discussed.

Çamlıbel, Mehmet Kanat (Dogus Author) This paper studies the disturbance decoupling problem for multi-agent systems with single integrator dynamics and a directed communication graph. We are interested in topological conditions that imply the disturbance decoupling of the network, and more generally guarantee the existence of a state feedback rendering the system disturbance decoupled. In particular, we will develop a class of graph partitions, which can be described as a "topological translation" of controlled invariant subspaces in the context of dynamical networks. Then, we will derive sufficient conditions in terms of graph partitions such that the network is disturbance decoupled, as well as conditions guaranteeing solvability of the disturbance decoupling problem. The proposed results are illustrated by a numerical example.

In this paper we study the disturbance decoupling problem for continuous piecewise affine systems. We establish a set of necessary conditions and a set of sufficient conditions, both geometric in nature, for such systems to be disturbance decoupled. Furthermore, we investigate mode-independent state feedback controllers for piecewise affine systems and provide sufficient conditions for the solvability of the disturbance decoupling problem by state feedback.

In this brief, we will study the computation of transient solutions of a class of piecewise- linear (PL) circuits. The network models will be so-called linear complementarity systems, which can be seen as dynamical extensions of the PL modeling structure as proposed by [1]. In particular, the numerical simulation will be based on a time-stepping method using the well-known backward Euler scheme. It will be demonstrated, by means of an example, that this widely applied time-stepping method does not necessarily produce useful output for arbitrary linear dynamical systems with ideal diode characteristics. Next the consistency of the method will be proven for PL networks that can be realized by linear passive circuit elements and ideal diodes by showing that the approximations generated by the method converge to the true solution of the system in a suitable sense. To give such a consistency proof, the fundamental framework developed in [2] is indispensable as it proposes a precise definition of a "solution" of a linear complementarity system and provides conditions under which solutions exist and are unique.

This paper deals with robust synchronization of undirected multi-agent networks with uncertain agent dynamics. Given an undirected network with identical nominal dynamics for each agent, we allow uncertainty in the form of coprime factor perturbations of the transfer matrix of the agent dynamics. We assume that these perturbations are stable and have H∞-norm that is bounded by some a priori given desired tolerance. In this paper, we derive state space equations for dynamic observer based protocols that achieve synchronization in the presence of such perturbations. We show that this robust synchronization of the network by the dynamic protocol is equivalent to robust stabilization of a single linear system by all controllers from a related finite set of feedback controllers. Our protocols are expressed in terms of real symmetric solutions to certain algebraic Riccati equations, and contain weighting factors depending on the eigenvalues of the graph Laplacian. We show that in this class of dynamic protocols, one can achieve a guaranteed tolerance that is proportional to the square root of the quotient of the smallest and the largest eigenvalue of the graph Laplacian.

Çamlıbel, Mehmet Kanat (Dogus Author) In this paper we present observer and output-based controller design methods for linear complementarity systems (LCS) employing a passivity approach. Due to various inherent properties of LCS, such as the presence of state jumps, mode dynamics described by differential and algebraic equations (DAEs), and regions for certain modes being lower dimensional, various observer and control design schemes that have been proposed for other classes of (hybrid) dynamical systems do not apply to LCS. In particular, we present an observer design method for LCS which is effective even in the presence of state jumps. We show the well-posedness of the observer, in the sense of existence and uniqueness of solution trajectories for the estimated state, and prove the global exponential stability of the observation error. These two properties guarantee that the estimated state exponentially recovers the state of the system. For the problem of stabilization based on output measurements only, we adopt an observer-based control approach in which we apply a state feedback law to the estimated state obtained from the observer. We prove that the resulting closed-loop system is well-posed and globally exponentially stable. In order to show the well-posedness of the closed loop, novel well-posedness results for LCS based on low-index properties are presented.

In this paper, first, balanced truncation of linear systems is revisited. Then, simultaneous balancing of multiple linear systems is investigated. Necessary and sufficient conditions are introduced to identify the case where simultaneous balancing is possible. The validity of these conditions is not limited to a certain type of balancing, and they are applicable for different types of balancing corresponding to different equations, like Lyapunov or Riccati equations. The results obtained are used for model order reduction of switched linear systems (SLS) by simultaneous balanced truncation. Finally, we give conditions under which global uniform exponential stability is preserved after simultaneous balanced truncation of the original switched linear system.

The main object of study in this paper is the class of switched linear systems, i.e. a collection of linear input/state/output systems and a set of switching signals that determine the active subsystem from the collection at any given time instant. We address the problem of left-invertibility for these systems. Left-invertible switched linear systems are those for which one can recover the switching signal (up to an equivalence class) and the input uniquely from a given output of the system. After introducing an equivalence relation for switching signals, we give precise definition of left-invertibility based on this equivalence relation. By taking a geometric approach, the paper presents a set of necessary and sufficient conditions for left-invertibility. These conditions are linear in nature and can be checked by using the techniques from geometric approach to linear systems.

Çamlıbel, Mehmet Kanat (Dogus Author) -- Conference full title: 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009; Shanghai; China; 15 December 2009 through 18 December 2009 Instantaneous charge/flux transfers may occur in switched electrical circuits when the switch configuration changes. Characterization of such state discontinuities is a classical issue in circuit theory which, typically, is based on the so-called charge and flux conservation principle. This paper proposes a general state transfer principle for arbitrary switching port-Hamiltonian systems. This new principle coincides with the charge and flux conservation principle in the special case of linear RLC circuits, but also covers circuits with nonlinear capacitors and inductors, and of arbitrary topology. Moreover, the new principle is applied to switching mechanical systems.

This paper studies open-loop stabilization problem for bimodal systems with continuous vector field. It is based on the earlier work of the authors on the controllability problem for the same class of systems. A full characterization of stabilizability is established by presenting algebraic necessary and sufficient conditions. It is also shown that controllability implies stabilizability for these systems in a very similar fashion to the linear case. (c) 2008 Published by Elsevier Ltd.

The problem of checking certain controllability prop erties of even very simple piecewise linear systems is known to be undecidable. This paper focuses on conewise linear systems, i.e. systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions. For this class of systems, we present algebraic necessary and sufficient conditions for controllability. We also show that the classical results of controllability of linear systems and input-constrained linear systems can be recovered from our main result. Our treatment employs tools both from geometric control theory and mathematical programming. IEEE Control Systems Society

This paper presents necessary and sufficient conditions for null controllability of discrete-time linear systems subject to both input and state constraints. The classical results for linear systems without constraints by Kalman and Hautus and for linear systems with only input constraints by Evans, Nguyen and Sontag can be obtained from our main result as particular cases.

This paper presents necessary and sufficient conditions for controllability of linear systems subject to input/state constraints.

This paper studies controllability of bimodal systems that consist of two linear dynamics on each side of a given hyperplane. We show that the controllability properties of these systems can be inferred from those of linear systems for which the inputs are constrained in a certain way. Inspired by the earlier work on constrained controllability of linear systems, we derive necessary and sufficient conditions for a bimodal piecewise linear system to be controllable.

The object of study of this paper is the class of hybrid systems consisting of so-called linear complementarity (LC) systems, that received a lot of attention recently and has strong connections to piecewise affine (PWA) systems. In addition to PWA systems, some of the linear or affine submodels of the LC systems can 'live' at lower-dimensional subspaces and re-initializations of the state variable at mode changes is possible. For LC systems we study the stability and controllability problem. Although these problems received for various classes of hybrid systems ample attention, necessary and sufficient conditions, which are explicit and easily verifiable, are hardly found in the literature. For LC systems with two modes and a state dimension of two such conditions are presented. IEEE; SIAM; Control Syst Soc; SICE; Informs; Honeywell Lab; Natl Instruments; XEROX; MathWorks

We study the notion of passivity in the context of complementarity systems, which form a class of nonsmooth dynamical systems that is obtained from the coupling of a standard input/output system to complementarity conditions as used in mathematical programming. In terms of electrical circuits, the systems that we study may be viewed as passive networks with ideal diodes. Extending results from earlier work, we consider here complementarity systems with external inputs. It is shown that the assumption of passivity of the underlying input/output dynamical system plays an important role in establishing existence and uniqueness of solutions. We prove that solutions may contain delta functions but no higher-order impulses. Several characterizations are provided for the state jumps that may occur due to inconsistent initialization or to input discontinuities. Many of the results still hold when the assumption of passivity is replaced by the assumption of "passifiability by pole shifting". The paper ends with some remarks on stability.