BIBO Stability of Continuous Time Systems

In this paper, the problems of the stability analysis and BIBO stabilization for the switched systems are considered. Applying a stabilizing local state feedback to each subsystem, the sufficient conditions of the asymptotically stable and BIBO stabilization for the switched systems are obtained by means of the method of Lyapunov function and the method of inequality analysis.

AAK Theorem and a Design of Multidimensional BIBO Stable Filters

Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.

ADRC based control for a class of input time delay systems

This paper is concerned with the control design and the theoretical analysis for a class of input time-delay systems with stable, critical stable or unstable poles. In order to overcome the time delay, a novel feed-forward compensation active disturbance rejection control(FFC-ADRC) approach is proposed. It combines advantages of the Smith predictor and the traditional active disturbance rejection control(ADRC). The tracking differentiator(TD) is designed to predict the control signal, which adds an anticipatory control to the control signal and allows a higher observer bandwidth to obtain better disturbance rejection. The modified extended state observer(ESO) is designed to estimate both system states and the total disturbances(internal disturbance, uncertainties and delayed disturbance). Then the Lyapunov theory and the theory of the input-output stability are applied to prove the asymptotic stability of the closed-loop control system. Finally, numerical simulations show the effectiveness and practicality of the proposed design.

Model Implementation and Analysis of a True Three-dimensional Display System

To model a true three-dimensional(3D)display system,we introduced the method of voxel molding to obtain the stereoscopic imaging space of the system.For the distribution of each voxel,we proposed a four-dimensional(4D)Givone–Roessor(GR)model for state-space representation—that is,we established a local state-space model with the 3D position and one-dimensional time coordi-nates to describe the system.First,we extended the original elementary operation approach to a 4D condition and proposed the implementation steps of the realiza-tion matrix of the 4D GR model.Then,we described the working process of a true 3D display system,analyzed its real-time performance,introduced the fixed-point quantization model to simplify the system matrix,and derived the conditions for the global asymptotic stability of the system after quantization.Finally,we provided an example to prove the true 3D display system’s feasibility by simulation.The GR-model-representation method and its implementation steps proposed in this paper simplified the system’s mathematical expression and facilitated the microcon-troller software implementation.Real-time and stability analyses can be used widely to analyze and design true 3D display systems.

Stability Analysis of Parallel Fuzzy P + Fuzzy I + Fuzzy D Control Systems

The study presented in this paper is in continuation with the paper published by the authors on parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative （FP ＋ FI ＋ FD） controller. It addresses the stability analysis of parallel FP ＋ FI ＋ FD controller. The famous＂small gain theorem＂ is used to study the bounded-input and bounded-output （BIBO） stability of the fuzzy controller. Sufficient BIBO-stability conditions are developed for parallel FP ＋ FI ＋ FD controller. FP ＋ FI ＋ FD controller is derived from the conventional parallel proportional plus integral plus derivative （PID） controller. The parallel FP ＋ FI ＋ FD controller is actually a nonlinear controller with variable gains. It shows much better set-point tracking, disturbance rejection and noise suppression for nonlinear processes as compared to conventional PID controller.

The Learning Control and Learning Adaptive Control of General Nonlinear Systems：MIMO Case

The learning control law for the general MIMO nonlinear systems with white noise distrubance is presented in the paper,it has extremely simple, recursive, incremental form,and strong robustness,it can also deal with the ill-conditioned systems.The new adaptive control scheme is presented when the parameters of the MIMO nonlinear systems are unknown.The convergence,BIBO stability,and robustness of learning adaptive control scheme are also discussed in this paper.