New results on reachable set bounding for linear time delay systems with polytopic uncertainties via novel inequalities

Abstract

This work is further focused on analyzing a bound for a reachable set of linear uncertain systems with polytopic parameters. By means of L-K functional theory and novel inequalities, some new conditions which are expressed in the form of LMIs are derived. It should be noted that novel inequalities can improve upper bounds of Jensen inequalities, which yields less conservatism of systems. Consequently, some numerical examples demonstrate that the authors’ results are somewhat more effective and advantageous compared with the previous results.

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

“…Therefore, extensive research is devoted to the study of the reachable set estimation issue of dynamic systems with delay. During the past few decades, there have been some excellent results related to the reachable set estimation of time-delay systems [11,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Reachable Set Estimation for Uncertain Markovian Jump Systems with Time-Varying Delay and Disturbances

“…In recent years, the problem of reachable set estimation for time-delay systems has attracted much attention. en, an increasing number of researchers have devoted their efforts to the problem of reachable set estimation [7][8][9][10][11]. In [7], a delay-dependent condition for an ellipsoid bounding the set of reachable states was presented by using the Lyapunov-Razumikhin function and the S-procedure.…”

“…Based on a relaxed Lyapunov-Krasovskii function, the delay-dependent and delay-rate-dependent conditions for the existence of a desired ellipsoid are obtained [8]. Chen and Zhong [10] studied the reachable set of neutral systems with perturbations and uncertainties via novel inequality. In [11], the time-varying delay is split into two nonuniform subintervals based on the Lyapunov-Krasovskii functional, and using the well-known Wirtinger integral inequality and reciprocating convex combination inequality, the RSE boundary of the time-delay system is obtained.…”

On reachable set estimation of nonlinear singular systems with distributed delay

“…It has been widely studied for singular systems with time‐varying delay, 29,30 T‐S fuzzy systems, 31 and linear systems with time‐delay 32‐37 . The problems on RSE for linear systems with polytopic parameter uncertainties 38,39 and Markov jump linear parameter‐varying (LPV) systems are considered 40 . Improved results of reachable set estimation and synthesis are reported 41 .…”