Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Fault Estimation for a Class of Markov Jump Piecewise-Affine Systems: Current Feedback Based Iterative Learning Approach

In this paper, the issues of stochastic stability analysis and fault estimation are investigated for a class of continuoustime Markov jump piecewise-affine(PWA) systems against actuator and sensor faults. Firstly, a novel mode-dependent PWA iterative learning observer with current feedback is designed to estimate the system states and faults, simultaneously, which contains both the previous iteration information and the current feedback mechanism. The auxiliary feedback channel optimizes the response speed of the observer, therefore the estimation error would converge to zero rapidly. Then, sufficient conditions for stochastic stability with guaranteed performance are demonstrated for the estimation error system, and the equivalence relations between the system information and the estimated information can be established via iterative accumulating representation.Finally, two illustrative examples containing a class of tunnel diode circuit systems are presented to fully demonstrate the effectiveness and superiority of the proposed iterative learning observer with current feedback.