Chunbo Feng

Reduced-Order Controllers for Singular H∞ Control Problems Based on LMI

Abstract In this paper an linear matrix inequality (LMI) approach for designing the reduced-order controllers for singular H ∞ control problems is proposed. For the singular case where the direct feedthrough from the input to the error and from the exogenous signal to the output are no longer of full rank, it is proved that reduced-order controllers with orders less than the generalized plant order exist if the singular H ∞ control problems are solvable. An algorithm for constructing the controllers is given. In comparison with previous results, no assumption about zeros on finite imaginary-axis is needed in this paper.

Reduced-order output feedback controllers for the robust H∞ performance problem

ConclusionThis note considers robust H∞ control problems for a class of systems with time-varying uncertainty lying in a hyperrectangle. It has two features: (i) Output feedback controllers are discussed instead of the state feed-back ones. It is proved that the problem can be reduced to finite-dimensional convex programming problems of finite vertex LMIs. All desired output feedback controllers can be parameterized based on the solutions of 2m LMIs. (ii) Reduced-order controller design is considered and the design idea is also formulated as solutions to LMIs. These results are also an extension of the main theorems about reduced-order controllers discussed in ref. [8] for uncertain systems. Based on the approaches presented here, similar problems in the discrete-time case could be dealt with.

Variable structure control for MRAC systems with perturbations in input and output channels

A design scheme of variable structure model reference control systems using only input and output measurements is presented for the systems with unmodeled dynamics and disturbances in input and output channels. The modeled part of the systems has relative degree greater than one and unknown upper bound of degree. By introducing some auxiliary signals and normalized, signals with memory functions and appropriate choice of controller parameters, the developed variable structure controller guarantees the global stability of the closed-loop system and the arbitrarily small tracking error.

Calculation of eigenvalues and their distribution for linear systems

Two methods for calculating eigenvalues of linear systems are proposed. One is to use the root locus method to calculate the eigenvalues step by step from low order systems to high order systems. The other is to use the property of Schwartz matrix to determine the factors of the characteristic equation by the searching method. A method for determining the number of eigenvalues in each half complex plane is also presented.

Robust H~∞ controller design for a class of uncertain systems

TheH∞ control problem for a class of systems with time-varying and nonlinear uncertainties is considcred. A new sufficient condition based on LMI is provided to judge their robust stability andL2-gain finiteness. Solvability conditions are presented for both state feedback and output feedback cases, which are all reduced to solutions of LMIs. The design procedure is also discussed via LMI approach.

Fuzzy Sliding Mode Control for Uncertain Dynamic Systems via Output Feedback

Abstract A scheme of fuzzy control for a class of uncertain dynamic systems with nonlinear unmodeled dynamics and external disturbances is presented in this paper. The design is based on the principle of variable structure control. Only the output signal is used in the control scheme. By using Lyapunov method, the closed-loop controlled system is proven to be globally BIBO stable. Simulation shows that the chattering phenomenon which is inherent to a sliding mode control is avoided, and the fuzzy control system exhibits strong robustness against model uncertainties and external disturbances.

Stable adaptive fuzzy control for a class of interconnected systems

Abstract The problem of adaptive fuzzy control for a class of interconnected systems with both unknown constant control gains and unknown function control gains is studied in this paper. By using fuzzy modeling method, a design scheme of stable adaptive fuzzy controller is proposed. According to the Lyapunov method, the closed-loop fuzzy control system is proved to be globally stable, with tracking errors conversing to a neighborhood of zero. Finally, the simulation results are given to demonstrate the effectiveness of the approach.

An LMI-based unified approach to reduced-order controller design

The design of reduced-order controllers is considered for stabilization control, covariance upper bound control, linear quadratic regulator, ℒ∞ control,H∞ control, positive real control problems and robustH2 control, robust ℒ∞ control and robustH∞ control problems for generalized linear plants without any additional assumptions. An upper bound of the order is obtained with which the (robust) controllers can guarantee stability constraints and satisfy the same design objectives as the so-called “full-order” controllers. A unified linear-matrix-inequality (LMI) based approach to reduced-order (robust) controller design for all the above-mentioned problems is provided. It is shown that each of these problems is solvable if and only if two uncoupled LMIs with an LMI-type constraint have a pair of positive definite solutions, one of which has a lower dimension than that given by Skelton and Iwasaki (1995). All desired reduced-order (robust) controllers are parameterized via the solutions of LMIs. Moreover, a design procedure is proposed based on the above LMI approach.

Robust Stability of MIMO Systems with Nonlinear and Linear Structured Uncertainties

Abstract In the first part of this paper, the multivariable Popov criterion of stability is extended to nonlinear systems with structured dynamic uncertainty. In the second part of the paper, a general approach based upon stability multiplier and loop transformation is given for seeking the mixed μ upper bounds.

Singularity–Free Decentralized Adaptive Control of Interconnected Systems

Abstract A new indirect decentralized adaptive control algorithm for discrete-time system is presented in this paper. The key idea in the algorithm is to design local controller such that each subsystem is independently controlled in some extent and to have no any singularities. Global boundedness of all signals for the whole closed loop system is guaranteed in the presence of interconnections, unmodelled dynamics and bounded disturbances of the subsystems. The algorithm needs neither the restrictions on plant parameters, and zeros nor the introduction of persistent excitation.