Robust Stability Analysis of a Class of LTV Systems

Many physical systems are inherently time-varying in nature. When these systems are linearized around a trajectory, generally, the resulting system is Linear Time-Varying (LTV). LTV systems describe an important class of linear systems and can be thought of as a natural extension of LTI systems. However, it is well known that, unlike LTI systems, the eigenvalues of an LTV system do not determine its stability. In this paper, the stability conditions for a class of LTV systems are derived. This class is composed of piecewise LTV systems, i.e. LTV systems that are piecewise linear in time. Sufficient conditions of stability are derived in the form of linear matrix inequalities (LMIs) by using the Lyapunov stability criterion. The feasibility of LMIs guarantees the stability of a given piecewise LTV system. Furthermore, uncertain piecewise LTV systems with scalar parametric uncertainty are also considered. Sufficient conditions for robust stability of this case are also presented, which come out to be quasi-LMIs, which can be optimized using a bisection algorithm to find the bounds of uncertainty for which the system is stable. The proposed method is applied to the problem of pitch angle control of a space launch vehicle, and the results are presented.Comment: Presented at 20th International Bhurban Conference on Applied Sciences and Technology (IBCAST), 202

Razumikhin and Krasovskii stability of impulsive stochastic delay systems via uniformly stable function method

This paper generalizes Razumikhin-type theorem and Krasovskii stability theorem of impulsive stochastic delay systems. By proposing uniformly stable function (USF) in the form of impulse as a new tool, some properties about USF and some novel pth moment decay theorems are derived. Based on these new theorems, the stability theorems of impulsive stochastic linear delay system are acquired via the Razumikhin method and the Krasovskii method. The obtained results enhance the elasticity of the impulsive gain by comparing the previous results. Finally, numerical examples are given to demonstrate the effectiveness of theoretical results

Detectability Conditions and State Estimation for Linear Time-Varying and Nonlinear Systems

This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the system. This allows for an observer design with low computational complexity compared to classical estimation approaches. An extension of this observer design to a class of nonlinear systems is proposed and local convergence of the corresponding estimation error dynamics is proven. Numerical results show the efficacy of the proposed observer design technique