In this paper, we investigate the interval observer problem for a class of discrete-time nonlinear systems, in absence or presence of external disturbances and parametric uncertainties. The interval observers depend on the design of two preserving order observers, providing lower and upper estimations of the state. The main objective is to apply the stability radii notions and cooperativity property in the estimation error systems in order to guarantee that the lower/upper estimation is always below/above the real state trajectory at each time instant from an appropriate initialization, and the estimation errors converge asymptotically towards zero when the disturbances and/or uncertainties are vanishing. For the disturbed case, the estimation errors practically converge to a vicinity of zero, while the lower/upper estimations preserve the partial ordering with respect to the state trajectory. The design conditions, that are valid for Lipschitz nonlinearities, can be expressed as Linear Matrix Inequalities (LMIs). A numerical simulation example is provided to verify the effectiveness of the proposed method.

This paper presents an adaptive strategy to solve the formation control problem for a set of second-order agents with parametric uncertainty and nonlinearity. The strategy regards a group of agents where the nonlinearities and uncertainties are represented by a linearly parametrized term, which allows us to consider non-identical agents. In order to ensure the collision-free motion of agents, we propose the use of a repulsive vector field component that is applied only when a pair of agents becomes nearer than a predefined minimum bound. Numerical simulations were carried out to show the effectiveness of the proposed scheme. First, a simplified example was used to verify the key features of the control law, followed by a general case to illustrate the performance of the algorithm in a more complex scenario.

This paper presents an adaptive strategy to solve the formation control problem for a set of second-order agents with parametric uncertainty and nonlinearity. The strategy regards a group of agents where the nolinearities and uncertainties are represented by a linearly parametrised term, which allows us to consider non-identical agents. In order to ensure the collision-free motion of agents, we propose the use of a repulsive vector field component that is applied only when a pair of agents become nearer than a predefined minimum bound. Numerical simulations were carried out to show the effectiveness of the proposed scheme, first with a simplified example to verify the key features of the control law and a general case to illustrate the performance of the algorithm in a more complex scenario.

This paper proposes a methodology for designing full-order and reduced-order interval observers for Linear Time-Invariant (LTI) systems, in both continuous and discrete-time settings, in the presence of uncertainties, disturbances, and measurement noise. The class of systems considered requires that the number of independent measured outputs be greater than or equal to the number of unmeasured states. The proposed approach enables the constructive assignment of the state matrix of the estimation error dynamics over the admissible Metzler–Hurwitz class compatible with the observer structure through an appropriate selection of the observer gains, ensuring both stability and cooperativity conditions without requiring the solution of Linear Matrix Inequalities. This flexibility facilitates the design of full and reduced-order interval observers for both continuous and discrete-time cases, generating upper and lower estimates that enclose the true state trajectory. Numerical examples are presented to illustrate the effectiveness of the proposed interval observer design methodology.