Chen-Fa Hsu

Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equation

Lower and upper bounds on the trace of the positive semidefinite solution of the algebraic matrix Riccati and Lyapunov equation are derived. The upper trace bound obtained in this note in many cases results in a tighter bound as compared to the Upper bound for the maximal eigenvalue proposed in [1] and [2].

Output tracking control of nonlinear systems with mismatched uncertainties

Abstract This paper addresses the output tracking problem of a class of nonlinear systems. Given input-output linearizability of the class of nonlinear systems, a robust output tracking controller derived via a Lyapunov-based approach is proposed. Here, the model uncertainties do not need to satisfy the conventional matching condition but states and tracking error remain bounded. Furthermore, the magnitude of the tracking error will bear dominant dependence on the magnitude of the mismatched uncertainties.

Root-locus approach to the stability analysis of interval matrices

A new approach, called the root-locus approach, is developed for the stability analysis of perturbed matrices. The basic idea of this approach is to ensure that the root loci of a continuously perturbed matrix remain in the open-left-half complex s-plane. Based on this approach, new techniques are presented to analyse the stability of interval matrices. Examples are given to demonstrate the merit of the proposed theorems.

New approach to time-domain analysis for stability robustness of dynamic systems

This paper presents a new approach to the analysis of the stability robustness of dynamic systems in state-space models. By continuously perturbing the state matrix, instead of solving the Lyapunov equation, an elegant stability robustness fundamental is derived. Subsequently, the allowable norm bound of the error matrix can be obtained under weakly structured perturbations, and the magnitude bound on individual elements of the error matrix can be obtained under highly structured perturbations. The merits of the theorems and corollary developed are demonstrated by two examples where the results achieved are much better than those already published in the literature. The concept that the perturbed state matrix would depend on the operating frequencies is also introduced.

Stability robustness analysis of digital control systems in state-space models

The stability robustness of discrete linear time-invariant systems in state-space models is analysed. Based on a root-locus approach and from the stable-eigenvalue viewpoint, fundamental criteria for testing the stability robustness of autonomous systems are derived and applied to the robustness analysis of multivariable feedback systems. Both the norm bound and the element bounds for the allowed perturbations are obtained. A stability robustness index is denned which is useful both for the analysis and synthesis of control systems.

Stability robustness analysis for state space models

Asymptotically stable linear time-invariant systems under perturbations are considered and analyzed for stability robustness. Based on continuously perturbing the state matrix, instead of solving Lyapunov equation, an elegant stability robustness fundamental is derived. Subsequently, the allowable norm bound for the error matrix is obtained under weakly structured perturbations, and the magnitude bounds on the individual elements of the error matrix are obtained under highly structured perturbations. The concept that the perturbed state matrix would actually depend on the operating frequencies is also introduced. The merits of our developed theorems are demonstrated by two examples, and our results are much better than those published in the literature.

Robust control design for linear systems with uncertain parameters

This paper presents an approach for the control of linear systems with parameter uncertainty. The parameter uncertainty under consideration is assumed to be unknown but bounded and can exist in both state and input matrices. Using the linear quadratic optimal control formulation, we consider a cost functional which is parameterized by uncertainties. An upper bound on the cost which is incurred by state feedback control and system uncertainties is obtained, and a linear state feedback law is found to minimize the upper bound. Furthermore, under the conditions presented in this paper the steady-state bound-minimizing control gain is shown to exist and the stability of the resultant closed-loop systems is guaranteed for all admissible uncertainties. Finally, a gradient search algorithm is proposed to find the optimal values of the free parameters which affect the cost upper bound. A numerical example is included to demonstrate the effectiveness of the proposed method.

Decoupling control of a bit missile by eigenstructure assignment

A Bank-To-Turn (BTT) missile has significant aerodynamic and inertial cross-coupling between the pitch, yaw and roll axes. An effective BTT missile control system must be able to reduce the dynamic interactions, and must also be capable of command tracking, disturbance rejection, and maintaining system stability for all flight conditions. A BTT control system is developed based on concepts of the closed-loop eigenvalue/ eigenvector assignment and the command generator tracking. The eigenvalue assignment results in the required closed-loop damping and frequencies whereas the eigenvector assignment provides the necessary dynamic decoupling. Guidance command is tracked by the BTT missile owing to a feedforward controller which is designed via the command generator tracking concept. Disturbance rejection capability and systems stability for six typical flight conditions for such a BTT missile control system are demonstrated by simulations.

Output feedback control of a flexible robot arm

In this paper, a method is proposed to control a flexible robot arm by using a special output feedback control law based on the truncated model. The proposed method is simple and easy to implement, it is robust to modal truncation and to parameter variation. Numerical simulation shows that the performance of the arm is satisfactory.

Sensitivity analysis of linear uncertain systems and its application in the synthesis of an insensitive linear regulator

In this paper a newly developed theory concerning the analysis of the trajectory sensitivity of linear uncertain systems is first reviewed. An index suggested by the theory is then introduced to represent the sensitivity of a system. Based on this index, we devise a method for synthesizing low-sensitivity constant-gain feedback regulators. Both academic illustrative and practical design examples are provided to explain these concepts and techniques.