In this work, the problem of preview saturated control (PSC) for constrained discrete-time delayed systems (CD-TDS) was investigated. First, using an input–output method, a discrete-time system with time-varying delays was formally eliminated, and a discrete-time system with constant time delay was obtained. Then, an augmented error system (AES) was constructed through an auxiliary signal related to state variables, which changed the problem of PSC transform into a problem of robust stability for the interconnected subsystem. Afterward, using the Lyapunov function and linear matrix inequality (LMI) technique, sufficient conditions for the robust stability of the closed-loop system and the design of the PSC laws were given. Finally, numerical simulations were performed, and they demonstrated the validity of the results presented in this paper.

In this study, we present a novel L 2 norm-based preview tracking controller design for discrete-time periodic linear parameter-varying (LPV) systems based on a linear fractional representation (LFR). It also proposes a robust controller design method using actions that are integral and preview to achieve excellent tracking performance and output constraints assuming that the reference signal may be previewe. First of all, an augmented error system (AES) with future knowledge about related signals was performed for a linear periodic system using LFR, transforming a control issue with the preview leading to a stability issue. The proposed conditions depend on using slack variables and decision matrices related to LFR to generate novel preview control. Second, Lyapunov functions dependent on parameters and full-block multipliers were addressed to achieve synthesis situations that are less conservative for discrete-time periodic LPV/LFR systems, which were expressed as linear matrix inequalities (LMIs) to produce reliable output and condition feedback with preview actions. In the end, the efficiency of the proposed control methods was demonstrated based on two numerical cases.

In present work, we investigated preview saturated control (PSC) regarding constrained discrete-time delayed systems (CD-TDS). First, using an input-output approach, discrete time-varying delay system was eliminated formally. Discrete-time system with constant time delay was gained. Then, an augmented error system (AES) was constructed through an auxiliary signal related to state variables, which changed the problem of PSC transform into a problem of robust stability for the interconnected subsystem. Afterwards, using linear matrix inequality (LMI) as well as Lyapunov function, sufficient robust stability conditions regarding closed-loop system and design of PSC laws were given. Finally, numerical simulations were performed, and they demonstrated our result validity that presented.

This paper investigates the finite-time preview saturated control problem for linear parameter-varying systems with input saturation. The external disturbances and input saturation, previewable reference signals, and parameter variations are considered simultaneously. First, using the error system method, we construct an augmented error system with previewed information. This transforms the finite-time preview saturated control problem into a finite-time stabilization problem. Next, static output-feedback controllers are used to guarantee the finite-time boundedness of the closed-loop system. Sufficient conditions guarantee the existence of the desired controllers are obtained using linear matrix inequalities. At last, we use a numerical simulation to show the proposed design method's effectiveness.

In this paper, the static output periodic preview control (SOPPC) problem of discrete-time periodic systems (D-TPSs) is proposed. First, an augmented error periodic system (AEPS) is derived by introducing auxiliary variables related to the system state and input. Consequently, the SOPPC problem is transformed into a stabilization problem. Second, sufficient conditions are derived to ensure asymptotic stability, and these conditions are extended to the D-TPSs with disturbance. Moreover, the corresponding solvability condition for the design of the SOPPC laws is proposed using linear matrix inequality (LMI). Finally, a numerical example is used to illustrate the effectiveness of the results.