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The conditions for state /output non-overshooting measured by the state /output 2-norm of discrete-time switched linear systems are addressed in this paper. As a switched linear system considered consists of several discrete-time linear time-invariant(LTI) systems, a sufficient and necessary condition for state non-overshooting of discrete-time LTI systems is derived firstly, and the non-overshooting region, which is a pair of 0-symmetrical cones, is defined and discussed. Then, using the idea of dividing the state space into distinct non-overshooting regions–a subsystem corresponding to a one, some conditions for state non-overshooting of discrete-time switched linear systems are inferred by using the well-known S-procedure. Finally, some output non-overshooting conditions were set up in a similar way.

This paper presents state regulation analysis for discrete-time LTI systems. Based on state 2-norm, the decreasing and non-overshooting regions are defined, and some key properties are discussed first. Later, all discrete-time LTI systems are classified into four categories depending on their state 2-norm monotonous properties, and a deep region partition is carried out for the fourth category systems, which is in the majority and the most complex cases. An example is given to illustrate the theory results at last.

Attitude measurement is an essential technology in projectile trajectory correction. Magnetometers have been used for projectile attitude measurement systems as they are small in size, lightweight, and low cost. However, magnetometers are seriously disturbed by the artillery magnetic field during launch. Moreover, the error parameters of the magnetometers, which are calibrated in advance, usually change after extended storage. The changed parameters have negative effects on attitude estimation of the projectile. To improve the accuracy of attitude estimation, the magnetometers should be calibrated again before launch or during flight. This paper presents a fast calibration method specific for a spinning projectile. At the launch site, the tri-axial magnetometer is calibrated, the parameters of magnetometer are quickly obtained by optimal ellipsoid fitting based on a least squares criterion. Then, the calibration parameters are used to compensate for magnetometer outputs during flight. The numerical simulation results show that the proposed calibration method can effectively determine zero bias, scale factors, and alignment angle errors. Finally, a semi-physical experimental system was designed to further verify the performance of the calibration method. The results show that pitch angle error reduces from 3.52&deg, to 0.58&deg, after calibration. The roll angle error is reduced from 2.59&deg, to 0.65&deg, Simulations and experimental results indicate that the accuracy of magnetometer in strap-down spinning projectile has been greatly enhanced, and the attitude estimation errors are reduced after calibration.