Stability and Stabilization of Discrete-Time T–S Fuzzy Systems With Stochastic Perturbation and Time-Varying Delay

Membership-dependent stability conditions for type-1 and interval type-2 T–S fuzzy systems

“…Specially for the stability problem of nonlinear systems, it can be reduced to the stability analysis of an equivalent T-S fuzzy model. Basic stability conditions in terms of linear matrix inequalities (LMIs) can be derived based on the Lyapunov stability theory [5,6]. In literature, lots of methods have been applied to reduce the analysis conservativeness [7], for example, the small scale gain theorem in [8], polynomial Lyapunov function and the sum-of-squares approach in [9], and piecewise smooth quadratic (PSQ) Lyapunov function approach in [10].…”

Robust guaranteed cost state estimation for discrete‐time systems with random delays and random uncertainties

“…[1][2][3][4][5] In particular, when implementing the delayed continuous-time systems for computer simulation, it becomes essential to formulate discrete-time system that is an analogue of the continuous-time delayed systems. So in recent years, the researchers eventually paid attention for investigation on discrete-time systems, for details see previous studies [6][7][8][9][10] and references therein. In practice, discrete-time systems have found many applications, such as hydraulic, rolling mill systems, automatic control, secure communication, signal and image processing, chemical processes, and long transmission lines in pneumatic.…”

Stability analysis for discrete time-delay systems based on new finite-sum inequalities

“…The stability of discrete-time systems has attracted considerable attention from the system and control communities, and many significant results have recently been reported [4,16,22,25,32,33]. A time delay in a system is often a major cause of instability and poor system performance.…”

“…When deriving stability conditions for discrete-time systems with a constant delay, d, the constructed Lyapunov-Krasovskii functional V (k) usually contains 25 the term −1 j=−d k−1 i=k+j η T (i)Rη(i). By calculating the forward difference of this term, we obtain…”