Irene Zorzan

On the consensus of homogeneous multi-agent systems with arbitrarily switching topology

Abstract In this paper we investigate the consensus problem under arbitrary switching for homogeneous multi-agent systems with switching communication topology, by assuming that each agent is described by a single-input stabilizable state–space model and that the communication graph is connected at every time instant. Under these assumptions, we construct a common quadratic positive definite Lyapunov function for the switched system describing the evolution of the disagreement vector, thus showing that the agents always reach consensus. In addition, the proof leads to the explicit construction of a constant state-feedback matrix that allows the multi-agent system to achieve consensus.

On the consensus problem with positivity constraints

In this paper we investigate the consensus problem for multi-agent systems, under the assumptions that the agents are homogeneous and described by a single-input positive state-space model, the mutual interactions are cooperative, and the static state-feedback law that each agent adopts to achieve consensus preserves the positivity of the overall system. Conditions that are either necessary or sufficient for the solvability of the positive consensus problem are provided. Under certain additional assumptions on the agents dynamics, equivalent conditions are derived. Several examples illustrate the paper results.

Stability and Stabilizability of Continuous-Time Linear Compartmental Switched Systems

In this paper, we introduce continuous-time linear compartmental switched systems and investigate their stability and stabilizability properties. By their nature, these systems are always stable. Necessary and sufficient conditions for asymptotic stability for arbitrary switching functions, and sufficient conditions for asymptotic stability under certain dwell-time conditions on the switching functions are proposed. Finally, stabilizability is thoroughly investigated and proved to be equivalent to the existence of a Hurwitz convex combination of the subsystem matrices, a condition that, for positive switched systems, is only sufficient for stabilizability.

On the Consensus of Homogeneous Multiagent Systems With Positivity Constraints

This paper investigates the consensus problem for multiagent systems, under the assumptions that the agents are homogeneous and described by a single-input positive state-space model, the mutual interactions are cooperative, and the static state-feedback law that each agent adopts to achieve consensus preserves the positivity of the overall system. Necessary conditions for the problem solvability, which allow us to address only the special case when the state matrix is irreducible, are provided. Under the irreducibility assumption, equivalent sets of sufficient conditions are derived. Special conditions either on the system description or on the Laplacian of the communication graph allow us to obtain necessary and sufficient conditions for the problem solvability. Finally, by exploiting some results about robust stability either of positive systems or of polynomials, further sufficient conditions for the problem solvability are derived. Numerical examples illustrate the proposed results.

On the stabilizability of continuous-time compartmental switched systems

In this paper we introduce continuous-time positive switched systems, switching among autonomous compartmental subsystems. For this class of systems a set of interesting necessary and sufficient conditions for stabilizabilty is provided, based on the compartmental property of the subsystem matrices. In particular, it is shown that, differently from the general (i.e. noncompartmental) case, stabilizability is equivalent to the existence of a Hurwitz convex combination of the subsystem matrices.

State–feedback stabilization of multi-input compartmental systems

Abstract In this paper we address the positive (state–feedback) stabilization of multi-input compartmental systems, i.e. the design of a state–feedback matrix that preserves the compartmental property of the resulting feedback system, while achieving stability. We first provide necessary and sufficient conditions for the positive stabilizability of compartmental systems whose state matrix is irreducible. Then we address the case when the state matrix is reducible, identify two sufficient conditions for the problem solution, and then extend them to a general algorithm that allows to verify when the problem is solvable and to produce a solution.

L1 and H-infinity optimal control of positive bilinear systems

In this paper we consider L1 optimal and H-infinity optimal control problems for a particular class of Positive Bilinear Systems that arise in drug dosage design for HIV treatment. Starting from existent characterizations of the L1-norm for positive systems, a convex formulation for the first problem is provided. As for the H-infinity case, we propose an algorithm based on the iterative solution of a convex feasibility problem, that approximates an H-infinity optimal controller with arbitrary accuracy. A numerical example illustrates the results.

Continuous-Time Compartmental Switched Systems

In this chapter we investigate state-feedback and output-feedback stabilization of compartmental switched systems, under the additional requirement that the resulting switched system is in turn compartmental. Necessary and sufficient conditions for the solvability of the two problems are given. Subsequently, affine compartmental switched systems are considered, and a characterization of all the switched equilibria that can be “reached” under some stabilizing switching law \(\sigma \) is provided.

Positive Consensus Problem: The Case of Complete Communication

In this chapter the positive consensus problem for homogeneous multi-agent systems is investigated, by assuming that agents are described by positive single-input and continuous-time systems, and that each agent communicates with all the other agents. Under certain conditions on the Laplacian of the communication graph, that arise only when the graph is complete, some of the main necessary conditions for the problem solvability derived in [17, 18, 19] do not hold, and this makes the problem solution more complex. In this chapter we investigate this specific problem, by providing either necessary or sufficient conditions for its solvability and by analysing some special cases.