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This paper presents a robust nonlinear H∞ output-feedback control approach for attitude manoeuvring of flexible spacecraft with external disturbances, inertia matrix perturbation and input constraints. By applying Lyapunov stability theory and using the generalized S-procedure and sum of squares (SOS) techniques, the robust H∞ output-feedback attitude control problem is converted into a convex optimization problem with SOS constraints when the flexible spacecraft is modelled as a polynomial state-space equation with polytope uncertainties. As a result, it overcomes the difficulty in constructing Lyapunov function and implementing numerical computation caused by the non-convexity of output-feedback H∞ control design for nonlinear systems. Moreover, it enables the state-observer and the controller to be designed independently and hence the complexity of the control algorithm is reduced remarkably. A numerical example illustrates the effectiveness and feasibility of the proposed approach.

Summary This paper generalizes the existing finite‐time stability (FTS) analysis/synthesis research to nonlinear time‐varying systems in the nonlinear parameter‐varying (NPV) framework. Specifically, to guarantee both the transient and steady‐state performances for NPV systems with external disturbance and input constraints, concepts of mixed stability and mixed stability with H∞ disturbance attenuation are proposed, together with the corresponding analysis and synthesis methods. Differently from the existing FTS‐related works, the mixed stability in this paper consists of properties of uniform exponential stability in addition to FTS. Existence conditions for an nonlinear time‐varying controller to render an NPV system mixed stable with H∞ disturbance attenuation are given in terms of state‐and‐parameter–dependent linear matrix inequalities. The generalized S‐procedure is used to convexify the input constraints such that the resulting closed‐loop system satisfies the input constraints for any state starting from an admissible set. For the case that both parameters and state are subject to restricted regions, local synthesis results are also provided. All the conditions are in the form of state‐and‐parameter–dependent linear matrix inequalities, which can be efficiently solved by using sum‐of‐squares programming. A simulation example validates the effectiveness of the proposed approach.

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