## 1 Introduction
Moreover, in [38], for three classes of uncertain nonlinear MIMO systems, that are wider with respect to [21; 34; 35], including several manufacturing systems and land, sea and air transportation systems, subject to nonstandard disturbances and noises, some theorems are proved, that allow to design pseudo-PID controllers to track a sufficiently smooth reference signal with the tracking error norm smaller than a prescribed value. This paper, for a broad class of uncertain nonlinear MIMO systems much more general with respect to [34; 35; 38], provides a new and unified approach to design robust PD-type control laws without chattering to track a reference signal with bounded second derivative with the tracking error norm smaller than a prescribed value, despite the presence of bounded disturbances, parametric and structural uncertainties, and bounded measurement noises. With respect to [34], it is also proved that the proposed control laws are robust with respect to bounded measurement noises. With reference to the mechanical and transportation systems, this theory can be successfully applied when the controller uses as information: signals related to the joint space (obtainable with encoders, resolvers, or tachometric dynamos, for example) or signals related to the workspace (e.g., obtainable with cameras, sonar, or global positioning system (GPS)). Moreover, the proposed results are very useful also for the control of human-machine interaction (see e.g., [8; 15; 28]). The proposed control laws are based on the concept of majorant systems and result in establishing asymptotic bounds for the tracking error and its first derivative. The proposed controller design is based on two parameters. The first parameter is related to the minimum eigenvalue of a suitable matrix, on which the practical stability depends. The second parameter is easily related to the practical asymptotic stability region, the desired maximum tracking error norm, and its convergence velocity. If the tracked trajectories are not sufficiently smooth, suitable filtering laws are proposed to facilitate the implementation of the control laws and reduce the control magnitude, particularly during the transient phase. The designed controllers using the developed majorant systems technique allow one to obtain, in general, less conservative results; i.e., the actual tracking error is quite close to the error computed with the proposed methodology, unlike many other approaches based on unsuitable Lyapunov functions. This enables one to avoid significant technological problems such as, e.g., oversized amplifiers and actuators. The obtained theoretical results can be successfully applied to numerous theoretical and engineering applications (e.g., control of: rolling mills, conveyor belts, automatic guided vehicles (AGVs), unicycles, cars, trains, ships, airplanes, drones, missiles, satellites, manufacturing robots--welding, painting, assembly, pick and place for printed circuit boards, packaging and labeling, palletizing, product inspection, and testing-, surgical robots). The above systems are of great engineering relevance, e.g., nowadays AGVs have revolutionized the logistics and production organization, as they are innovative, versatile and cheap mobile robots very used in various processes (production and management of warehouses) for the loading, unloading, and/or transportation purposes. All the above mentioned systems fall into the considered broad class of systems and, therefore, can be effectively and simply controlled with the proposed laws in realistic situations and also by technicians not expert in the control field (see the easy and efficient control of the simple AGV considered in the Appendix A and, above all, the second and third applications in the paper). Concerning this, in the paper four significant applications are provided. The first one concerns the solution of a nonlinear equations system or the determination of an equilibrium point of a nonlinear systems.