This article deals with the consensus principle in a network of identical linear agents with strictly Metzler dynamics, when the considered communication topology is represented by an undirected graph. To guarantee the functionality of the observer-type consensus protocol, the design problem is parameterized using a structure of linear matrix inequalities, which reflects the principle of diagonal stabilization and singular decomposition of the Laplacian of the network topology graph. Design is clearly illustrated with an example.

The design conditions for multiplicative fault detection are presented in the paper. The direct effect of the occurrence of a multiplicative fault on the stability of the full-order observer is taken into account in the design procedure using an observer input adjusted to the vertical strip of the state-multiplicative faults. The task is parameterized in terms of linear matrix inequalities in the sense of the principle of norm bounded uncertainty constraints. In relation to the prescribed measurement structure, all details are given to illustrate the projection of the state estimation error into the fault residuals. The features of the proposed approach are shown in numerical example.

This paper focuses on the quadratic stabilization of one class of bilinear positive continuous-time systems subject to system disturbances. Using the quadratic Lyapunov function, new control design conditions are proposed as a set of linear matrix inequalities, which reflect the principle of diagonal stabilization and guarantee the quadratic stability and positivity of the closed-loop system. Taking into account an upper bound for the$\mathrm{H}_{\infty}$norm of the disturbance transfer function matrix, the task is redefined as a convex problem and it is shown that quadratic stabilization of the bilinear systems can be achieved by state feedback control. The key properties are illustrated by the detailed construction of the required system parameter structures in the example.

Determinate techniques for stabilization of the Takagi-Sugeno uncertain time-delay discrete-time systems with delayed information from sensors is the subject of this paper. By exploiting Lyapunov-Krasovskii functional, the new control design terms are placed in the domain and formulate the set of linear matrix inequalities, guaranteeing the closed-loop quadratic stability. Combining into the functional the disturbance transfer function$\mathbf{H}_{\infty}$norm upper bound, the cumulative task is defined as a multi-objective robust control problem. The key idea is to design a parallel structure of the fuzzy controller realization, while only the time-invariant control law gains are used. The problem is illustrated by an motivating example.

For linear discrete-time positive systems the paper proposes an approach reflecting local and global matrix structural constraints and positiveness in solving the problem of positive interval observers design. The local common system parameter constraints are represented in the form of linear matrix inequalities, combined with a Lyapunov inequality, to guarantee the observer asymptotic stability and global matrix structural constraints. A numerical example is included to assess the feasibility of the proposed technique.

The design conditions for residual filter design, based on an unknown input observer structure for linear discrete-time state-multiplicative linear systems, is presented in the paper. By the proposed method, the design problem is parameterized in terms of linear matrix inequalities, related to an enhanced bounded real lemma structure. Related to the residual filters for the given class of state-multiplicative structures, the design steps are revealed in the example for projecting the state estimation error to fault residuals.

The linear matrix inequalities approach is proposed to discrete-time linear positive system control design, reflecting enhanced and D-stability region approaches. Coupling together the set of linear matrix inequalities warranting the system positive structure and the structure guaranteing circle D-stability, the design conditions are outlined to raise the positive closed-loop system, considering a nonnegative control gain matrix. Some related properties are deduced to demonstrate diagonal stabilizability of the positive systems.

The paper relates the design principle for fault detection filters devoted to a class of continuous-time Lipschitz systems. The reference model principle within incremental quadratic constraints is proposed to formulate a criterion for fault detection filters design. The design conditions are outhned in terms of linear matrix inequalities to posses a stable design framework.

The paper is concerned with the problem of reconfiguration to retain fault tolerance in control of linear continuous-time systems with system parameter faults. Following the concept of fault tolerant control systems the main idea is to use a model output as the reference to be followed when a fault occurs, while the nominal control loop is kept untouched and the nominal controller remains a part of the reconfigured control loop. The full state control tenet is proposed for nominal control strategy and the static output control principle for the compensation control law specification. Exploiting ü-stability circle regions, new conditions for control laws parameter design are introduced and proven and a cascade-like reconfiguration structure stability is analyzed in the paper. The results, offering the sufficient and necessary design conditions, are illustrated with a numerical example to note the effectiveness of the proposed approach.