This letter propose a new H∞ smoother (HIS) with a finite impulse response (FIR) structure for discrete-time state-space models. This smoother is called an H∞ FIR smoother (HIFS). Constraints such as linearity, quasi-deadbeat property, FIR structure, and independence of the initial state information are required in advance. Among smoothers with these requirements, we choose the HIFS to optimize H∞ performance criterion. The HIFS is obtained by solving the linear matrix inequality (LMI) problem with a parametrization of a linear equality constraint. It is shown through simulation that the proposed HIFS is more robust against uncertainties and faster in convergence than the conventional HIS.

In this letter, we propose a new H2 smoother (H2S) with a finite impulse response (FIR) structure for discrete-time state-space signal models. This smoother is called an H2 FIR smoother (H2FS). Constraints such as linearity, quasi-deadbeat property, FIR structure, and independence of the initial state information are required in advance to design H2FS that is optimal in the sense of H2 performance criterion. It is shown that H2FS design problem can be converted into the convex programming problem written in terms of a linear matrix inequality (LMI) with a linear equality constraint. Simulation study illustrates that the proposed H2FS is more robust against uncertainties and faster in convergence than the conventional H2S.

This letter presents parametric uncertainty bounds (PUBs) for stabilizing receding horizon H∞ control (RHHC). The proposed PUBs are obtained easily by solving convex optimization problems represented by linear matrix inequalities (LMIs). We show, by numerical example, that the RHHC can guarantee a H∞ norm bound for a larger class of uncertain systems than conventional infinite horizon H∞ control (IHHC).

This letter presents delayed perturbation bounds (DPBs) for receding horizon controls (RHCs) of continuous-time systems. The proposed DPBs are obtained easily by solving convex problems represented by linear matrix inequalities (LMIs). We show, by numerical examples, that the RHCs have larger DPBs than conventional linear quadratic regulators (LQRs).

This letter presents robustness bounds (RBs) for receding horizon controls (RHCs) of uncertain systems. The proposed RBs are obtained easily by solving convex problems represented by linear matrix inequalities (LMIs). We show, by numerical examples, that the RHCs can guarantee robust stabilization for a larger class of uncertain systems than conventional linear quadratic regulators (LQRs).

In this letter, we propose a new multi-step maximum likelihood predictor with a finite impulse response (FIR) structure for discrete-time state-space signal models. This predictor is called a maximum likelihood FIR predictor (MLFP). The MLFP is linear with the most recent finite outputs and does not require a prior initial state information on a receding horizon. It is shown that the proposed MLFP possesses the unbiasedness property and the deadbeat property. Simulation study illustrates that the proposed MLFP is more robust against uncertainties and faster in convergence than the conventional multi-step Kalman predictor.

This letter presents new delayed perturbation bounds (DPBs) for stabilizing receding horizon H∞ control (RHHC). The linear matrix inequality (LMI) approach to determination of DPBs for the RHHC is proposed. We show through a numerical example that the RHHC can guarantee an H∞ norm bound for a larger class of systems with delayed perturbations than conventional infinite horizon H∞ control (IHHC).