Asymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.
We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state-space representation. We put particular emphasis on two classes of inverses: the weak generalized inverse and the Moore-Penrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computational ingredient to determine generalized inverses is the orthogonal reduction of the system matrix pencil...
This paper presents an algebraic design theory for interconnected systems. Usual multivariable linear systems are described in a unified way. Both square and nonsquare plants and controllers are included in the study and an easy characterization of the achievable I/O (input-to-output) and D/O (disturbance-to-output) maps is presented through the use of appropriate controllers. Sufficient conditions of stability are given.
The paper presents fractional-order semilinear, continuous, finite-dimensional dynamical systems with multiple delays both in controls and nonlinear function . The constrained relative controllability of the presented semilinear system and corresponding linear one are discussed. New criteria of constrained relative controllability for the fractional semilinear systems with delays under assumptions put on the control values are established and proved. The conical type constraints are considered....
The problem of modelling the dynamics of confidence levels between two individuals is investigated. A model, based on a master equation approach, is developed and presented. An important feature of the model is that self-confidence is modelled along with its interaction with confidence towards others. Simulation results are presented.
The problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A computational scheme is provided for the design of a network of observation locations in a spatial domain that are supposed to be used while detecting changes in the underlying parameters of a distributed parameter system. The setting considered relates to a situation where from among...
This work deals with a two-dimensional inverse problem in the field of tomography. The geometry of an unknown inclusion has to be reconstructed from boundary measurements. In this paper, we extend previous results of R. Kress and his coauthors: the leading idea is to use the conformal mapping function as unknown. We establish an integrodifferential equation that the trace of the Riemann map solves. We write it as a fixed point equation and give conditions for contraction. We conclude with a series...
The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is studied. Local and global optimality of extremal trajectories is characterized. Lower and upper bounds on the first conjugate time are proved. The cut time is shown to be equal to the first Maxwell time corresponding to the group of discrete symmetries of the exponential mapping. Optimal synthesis on an open dense subset of the state space is described.
The simultaneous problem of consensus and trajectory tracking of linear multi-agent systems is considered in this paper, where the dynamics of each agent is represented by a single-input single-output linear system. In order to solve this problem, a distributed control strategy is proposed in this work, where the trajectory and the formation of the agents are achieved asymptotically even in the presence of switching communication topologies and smooth formation changes, and ensuring the closed-loop...
The paper presents an algorithm for the solution of the consensus problem of a linear multi-agent system composed of identical agents. The control of the agents is delayed, however, these delays are, in general, not equal in all agents. The control algorithm design is based on the -control, the results are formulated by means of linear matrix inequalities. The dimension of the resulting convex optimization problem is proportional to the dimension of one agent only but does not depend on the number...