Order‐dependent and delay‐dependent conditions for stability and stabilization of fractional‐order time‐varying delay systems using small gain theorem

Abstract

AbstractIn this paper, the stability and stabilization problems for fractional‐order time‐varying delay systems are investigated. Firstly, by casting the stability problem as one of robust stability analysis problems and utilizing the small gain theorem, an order‐dependent and delay‐dependent stability condition for fractional‐order time‐varying delay systems is developed. Taking advantage of the information of order and delay, the stability condition is less conservative than the existing results. Then, state feedback controllers that stabilize fractional‐order time‐varying delay systems are developed. To tackle the computational difficulty of the controller design method, a local optimization algorithm is proposed. Finally, numerical examples are provided to illustrate that the proposed criteria are valid and less conservative than the existing ones.