Fan-Chu Kung

Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach

The authors present a procedure for obtaining the memoryless linear state feedback control of uncertain dynamic delay systems. The uncertainties are time varying and within a given compact set. This method is an extension of the Riccati equation approach proposed by I.R. Petersen and C.V. Hollot (1986). The extension is straightforward. Also the uncertainties do not need to satisfy the matching conditions. >

An approach to systematic design of the fuzzy control system

Abstract This paper presents a new design method of fuzzy control system (FCS). The concept from the sliding mode control is adopted to construct fuzzy control scheme. If the original control rules are inappropriate, the adaptive mechanism will modify these rules according to the proposed algorithms. In particular, the structure of sliding surface provides a reasonable estimation to the universes of discourse on which the fuzzy control rules are based. Finally, an inverted pendulum system is used to demonstrate the availability of the proposed approaches.

D-stability analysis for discrete systems with a time delay

This paper first discusses the D-pole placement problem of discrete time-delay systems. Some criteria are proposed to ensure that all the closed-loop eigenvalues of discrete systems with a time delay are located inside a specific disk D(α, r) centered at (α, 0) with radius r. Then, several sufficient conditions for guaranteeing the D-stability of discrete time-delay systems subjected to parametric perturbations are presented. Both unstructured and highly structured parametric perturbations are considered. By these sufficient conditions, the tolerable parametric perturbation bounds that ensure all the closed-loop poles of discrete time-delay perturbed systems to remain inside the desired disk D(α, r) can be estimated. Finally, illustrative examples are given for demonstration.

Design of fuzzy controller for active suspension system

Abstract The control objective of an active suspension system is to produce excellent sprung mass isolation (i.e. ride quality), not too large a rattle space and good road holding ability. Due to the specific dynamics, the active suspension usually adopts a compromise control policy such as linear quadratic regulation (LQR) or linear quadratic Gaussian (LQG) to determine the feedback gains of the controller. In contrast to the full-state feedback control, a sliding mode fuzzy control strategy is employed to design a stable controller for a quarter-car model of the active suspension system. Motivated by the principle of singular perturbation, a systematic design approach is introduced and verified by computer simulation. It is shown that satisfactory performance can be achieved even if the system is under perturbed conditions.

Robust stabilization of a class of singularly perturbed discrete bilinear systems

This paper presents two kinds of robust controllers for stabilizing singularly perturbed discrete bilinear systems. The first one is an /spl epsi/-dependent controller that stabilizes the closed-loop system for all /spl epsi//spl isin/(0, /spl epsi//sub 0/*), where /spl epsi//sub 0/* is the prespecified upper bound of the singular perturbation parameter. The second one is an /spl epsi/-independent controller, which is able to stabilize the system in the entire state space for all /spl epsi//spl isin/(0, /spl epsi/*), where /spl epsi/* is the exact upper /spl epsi/-bound. The /spl epsi/* can be calculated by the critical stability criterion once the robust controller is determined. An example is presented to illustrate the proposed schemes.

Shifted Legendre series solution and parameter estimation of linear delayed systems

The finite-dimensional shifted Legendre polynomials expansion is applied to approximate the solution of linear time-invariant systems with time delay. An integration matrix and a delay matrix for the shifted Legendre vector are derived so that the solution of a linear time-delay state equation is reduced to the solution of a linear algebraic matrix equation. In addition, parameters of the delayed state equation are also estimated by using the shifted Legendre expansion and the least-squares method. Two examples are given to demonstrate the accuracy of this approach.

Stability bounds of singularly perturbed discrete systems

The authors propose a systematic approach to determine the exact stability bound of singularly perturbed discrete time systems. By combining three conditions of the critical stability criterion with a bialternate product for discrete-time systems, the stability problems of two types of singularly perturbed discrete-time systems can be solved via the derived scheme. Several examples are given to illustrate the proposed results.

A new result on the robust stability of uncertain systems with time-varying delay

A stability criterion for uncertain systems with time-varying delay is derived via the Lyapunov functional approach. By checking the Hamiltonian matrix and solving an algebraic Riccati equation, a new bound on allowable stability preserving nonlinear perturbations is presented. The result obtained here is shown to be less conservative than others reported in the literature.

A new approach for the robust stability of perturbed systems with a class of noncommensurate time delays

In this paper, based on the Lyapunov stability theorem, matrix measure, and norm inequalities, a new approach for the robust stability of perturbed systems with a class of noncommensurate time delays is presented. Two classes of linear parametric perturbations are treated: (1) unstructured; and (2) highly structured perturbations. Several concise sufficient conditions, delay-dependent or delay-independent, are proposed to guarantee the asymptotic stability and positive stability degree of the perturbed multiple time-delay systems. Finally, two numerical examples are given to demonstrate the applications of these quantitative results. >

Solution of integral equations using a set of block pulse functions

Abstract A set of the block pulse functions is applied to solve the Fredholms and the Volterras integral equations of the second kind. An algebraic equation in matrix form which is equivalent to the solution of the integral equation is developed. The approximate results are easily obtained by a few computations. An accurate solution canbe evaluated in a digital computer by solving the algebraic equation. Two examples are given.