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Eigenvalue-based Controllability Analysis of Mars Entry Guidance

Controllability is the fundamental concept for system analysis and control synthesis. In this paper, the properties of controllability, including its duality to observability, are studied for the linearized dynamic systems. Furthermore, a novel criterion for determining the degree of controllability (DoC) based on the eigenvalues of the Controllability Gramian is proposed, and certain normalization is made to constrain the range of the controllability index. Then, the proposed criterion is implemented to the controllability analysis of Mars entry guidance. The simulation results show that the DoC criterion can reveal the dominating factor in the longitudinal dynamics during the entry phase, and can thus help us to gain information about the controllability characteristics of the system along the nominal trajectories. Hence, the DoC criterion can function as an indicator for entry trajectory design the control system optimization.