Robustness of perturbed large-scale systems with local constant state feedback

Abstract

The robustness problem of perturbed large-scalesystems is considered. The nominal large-scale system is stabilized by a local constant state feedback u,(t) = k,Xi(t) and the local optimal control law ui(t) = -R i -I BJ PiXi(t), respectively. In the above two cases, bounds are obtained for an allowable non-linear time-invariant (or timevarying) perturbation such that the resulting closed-loop large-scale system remains stable. The special case of a linear perturbation is also treated here. Nomenclature IR n real vector space of dimension n AT transpose of the matrix A A i ( A) ith eigenvalue of the matrix A II A lis spectral norm of the matrix A i.e. IIA lis = max [)'i(A T A)]112 , ( m )112 i.e. Ilgll = J,lgil 2 ,

H∞ decentralized fuzzy model reference tracking control design for nonlinear interconnected systems

“…is and is (8) Hence, the fuzzy decentralized controller is given by (9) Substituting (9) into (3) yields the closed-loop decentralized control of the subsystem as the following:…”

Adaptive Fuzzy Sliding Mode Control For Time-Delay Uncertain Large-Scale Systems

“…Then, we adapt minimum approximation error i of utilizing the adaptive gain 3) , therefore, we can define adaptation error of minimum approximation error as =i-i (21) and the adaptation error of adaptive gain SiO is defined as 41 (22) 4;io = S;io -S;io (2 By taking the time derivative of both sides of (11), we obtain Si = in + c 1ein -l + cn, -2e2 + CHj -1il (23) Ui (t) + ±Z hi 'A -Xdin, (t) + ±Cl inj + ±Cn -2ei2 + eil 1=1 j=l Now, the control law can be chosen according to (7) with us) givenby: Consider the following parameter update laws: =c ),Is (25) Oj, = y2Si;(x1) (26) 41o 735 (27) where r1 72', and y3 are positive constants specified by the designer. The proposed control law will guarantee the asympotical stability for the error dynamics of (10), and it will be proved in the following theorem.…”

“…Theorem 1: For the subsystems consisting of (2), the decentralized adaptive fuzzy control law is chosen as (7) with (24), and consider the adaptation laws (25)- (27). If Assumptions 1-3 are satisfied, then the following properties are guaranteed:…”

“…Therefore, the problem of decentralized control oftime-delay large-scale systems has received considerable attention, and many approaches have been developed to investigate the stability and stabilization of time-delay large-scale systems. The task of effectively controlling large-scale system with time-delay interconnections is still one ofthe most interesting and challenging control problems [25]- [27].…”