This paper considers the problem of a three-axis flexible satellite attitude stabilisation subject to the vibration of flexible appendages and external environmental disturbances, which affect the rigid body motion. To solve this problem, a disturbance observer is proposed to estimate and thereby reject the flexible appendage vibration. Based on the H∞ and Linear Matrix Inequality (LMI) approach, a controller for spacecraft with flexible appendages is proposed to ensure robustness as well as attitude stability with high precision. Stability analysis of the overall closed-loop system is provided via the Lyapunov method. The simulation results of three-axis flexible spacecraft demonstrate the robustness and effectiveness of the proposed method.

We study the problem of pseudostate and static output feedback stabilization for singular fractional-order linear systems with fractional order $\unicode[STIX]{x1D6FC}$ when $0<\unicode[STIX]{x1D6FC}<1$. All the results are given by linear matrix inequalities. First, a new sufficient and necessary condition for the admissibility of singular fractional-order systems is presented. Then based on the admissible result, not only are sufficient conditions for designing pseudostate and static output feedback controllers obtained, but also sufficient and necessary conditions are presented by using different methods that guarantee the admissibility of the closed-loop systems. Finally, the effectiveness of the proposed approach is demonstrated by numerical simulations and a real-world example.

For cable-driven parallel manipulators (CDPMs), it is known that maintaining positive cable tension is critical in constraining the moving platform. Hence, the force-closure workspace of CDPMs represents a set of poses where the cable tensions can balance arbitrary external wrench applied on the moving platform, proposed by researchers. A new computation method for the force-closure workspace of CDPMs is developed in this paper, and the new method is realized by calculating the null space of the structure matrix and solving the linear matrix inequalities. The detailed calculation procedures of the force-closure workspace for the incompletely restrained, completely restrained, and redundantly restrained CDPMs are given, respectively, and the advantages of the new method are analyzed according to the time complexity. The simulation experiments of the force-closure workspace computation are implemented on a six-degree of freedom (6-DOF) CDPM with eight cables, and then the superiority of the new method over the existing algorithm is studied.

In this paper, we present sufficient conditions for global optimality of a general nonconvex smooth minimisation model problem involving linear matrix inequality constraints with bounds on the variables. The linear matrix inequality constraints are also known as “semidefinite” constraints which arise in many applications, especially in control system analysis and design. Due to the presence of nonconvex objective functions such minimisation problems generally have many local minimisers which are not global minimisers. We develop conditions for identifying global minimisers of the model problem by first constructing a (weighted sum of squares) quadratic underestimator for the twice continuously differentiable objective function of the minimisation problem and then by characterising global minimisers of the easily tractable underestimator over the same feasible region of the original problem. We apply the results to obtain global optimality conditions for optinusation problems with discrete constraints.

This paper deals with robust guaranteed cost control for a class of linear uncertain descriptor systems with state delays and jumping parameters. The transition of the jumping parameters in the systems is governed by a finite-state Markov process. Based on stability theory for stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost controllers is derived. In terms of the LMI (linear matrix inequality) approach, a linear state feedback controller is designed to stochastically stabilise the given system with a cost function constraint. A convex optimisation problem with LMI constraints is formulated to design the suboptimal guaranteed cost controller. A numerical example demonstrates the effect of the proposed design approach.