When threatened by a pursuer, an evading aircraft launches two defenders to accomplish a cooperative evasion, constituting a fouraircraft interception engagement. Under the assumption that the pursuing aircraft adopts the augmented proportional guidance law and first-order dynamics, a cooperative intercept mathematical model with an intercept angle constraint is established, allowing for the cooperative maneuvering of the evader. Based on the differential linear matrix inequality (DLMI), a controller design method of input and output finite time stability (IO-FTS) is proposed and applied to the aircraft's cooperative intercept scenario. A cooperation performance analysis is carried out for two cases: (1) two defenders intercept the pursuer with various intercept angle constraints, and (2) the evader acts in a lure role to cooperate with two defenders. The simulation results indicate that the proposed method of controller design has the ability to guarantee that the two defenders intercept the pursuer at the preassigned intercept angles. The cooperative intercept scenario with a lure role is shown to be a very effective method for reducing the maximum required acceleration for defenders, which confirms the availability and advantage of cooperation. The strong adaptability and robustness of the cooperative guidance law with respect to various initial launch conditions is also verified.
This paper discusses the finite-time output stability (FTOS) for the impulse switching linear system (SLS) when the norm-bounded state constraint is simultaneously considered during a scheduled finite-time period. This system is a typical hybrid system whose state trajectory instantaneously jumps according to a predetermined resetting law. The sufficient conditions of both state boundedness and output stability are proposed for the SLS in finite-time period when two typical classes of input signals are involved. Based on the linear matrix inequality, the design method of a controller using state feedback is represented to ensure state boundedness and output stability concurrently for the closed-loop system, which can effectively avoid states and the output reaching large and unacceptable values at certain points in finite time. An effective solution to the controller using a linear discretization approach is also achieved. The two simulation examples verify the proposed methods.
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