Pradeep Misra

On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions

Abstract The aim of this paper is to address consensus and bipartite consensus for a group of homogeneous agents, under the assumption that their mutual interactions can be described by a weighted, signed, connected and structurally balanced communication graph. This amounts to assuming that the agents can be split into two antagonistic groups such that interactions between agents belonging to the same group are cooperative, and hence represented by nonnegative weights, while interactions between agents belonging to opposite groups are antagonistic, and hence represented by nonpositive weights. In this framework, bipartite consensus can always be reached under the stabilizability assumption on the state-space model describing the dynamics of each agent. On the other hand, (nontrivial) standard consensus may be achieved only under very demanding requirements, both on the Laplacian associated with the communication graph and on the agents’ description. In particular, consensus may be achieved only if there is a sort of “equilibrium” between the two groups, both in terms of cardinality and in terms of the weights of the “conflicting interactions” amongst agents.

Computation of structural invariants of generalized state-space systems

In this paper, we develop an algorithm for computing the zeros of a generalized state-space model described by the matrix 5-tuple (E,A, B, C, D), where E may be a singular matrix but det (A - hE) ¢- 0. The characterization of these zeros is based on the system matrix of the corresponding 5-tuple, Both the characterization and the computational algorithm are extensions of equivalent results for state-space models described by the 4-tuples (A,B, C,D). We also extend these results to the computation of infinite zeros, and left and right minimal indices of the system matrix. Several non-trivial numerical examples are included to illustrate the proposed results.

On the discrete generalized Lyapunov equation

Abstract In this paper we study the discrete generalized Lyapunov equation for implicit systems. We show how the anticipation phenomenon and the asymptotic stability of the system can be studied in terms of the solutions to the discrete generalized Lyapunov equation. We further study under which conditions these solutions are unique. Numerical examples are provided to illustrate the results presented.

On the Stabilizability and Consensus of Positive Homogeneous Multi-Agent Dynamical Systems

In this note we consider a supervisory control scheme that achieves either asymptotic stability or consensus for a group of homogenous agents described by a positive state-space model. Each agent is modeled by means of the same SISO positive state-space model, and the supervisory controller, representing the information exchange among the agents, is implemented via a static output feedback. Necessary and sufficient conditions for the asymptotic stability, or the consensus of all agents, are derived under the positivity constraint.

Time-invariant representation of discrete periodic systems

A large number of results from linear time-invariant system theory can be extended to periodic systems provided an equivalent time-invariant system can be found. This paper presents a simple and numerically reliable procedure to achieve the same. It is shown that, using a stacked representation of periodic systems, under system equivalence, a minimal-order generalized state-space description can always be obtained.

Finite-dimensional approximations of unstable infinite-dimensional systems

This paper studies approximation of possibly unstable linear time-invariant infinite-dimensional systems. The system transfer function is assumed to be continuous on the imaginary axis with finitely many poles in the open right half plane. A unified approach is proposed for rational approximations of such infinite-dimensional systems. A procedure is developed for constructing a sequence of finite-dimensional approximants, which converges to the given model in the

Hessenberg-triangular reduction and transfer function matrices of singular systems

L_\infty

A computational algorithm for squaring-up. I. Zero input-output matrix

norm under a mild frequency domain condition. It is noted that the proposed technique uses only the FFT and singular value decomposition algorithms for obtaining the approximations. Numerical examples are included to illustrate the proposed method.

Computational of minimal-order realizations of generalized state-space systems

The author is concerned with the computation of transfer function matrices of liner multivariable systems described by their generalized state-space equations. An algorithm is outlined that may be considered a generalization of an existing technique for computation of transfer matrices of systems described by standard state-space equation. The propose algorithm can be used for evaluating transfer function matrices of nonsingular as well as singular generalized systems, and performs satisfactorily when implemented with finite-precision arithmetic. Several examples are included to demonstrate the performance of the proposed algorithm. >

Computation of Stable Invariant Subspaces of Hamiltonian Matrices

Some preliminary results on the problem of squaring-up a nonsquare linear multivariable system are presented. It is shown that, for the case considered here, the squaring-up problem can be transformed into a state feedback problem. The proposed approach ensures that the resulting squared system can retain the existing zeros where they were located and assign any additional zeros at desired locations. A numerical example is included to illustrate the results developed.<<ETX>>