On a stability theorem for nonlinear systems with slowly varying inputs

Recently, M. Kelemen (IEEE Trans. Automat. Contr., vol.AC-31, 766-768, Aug. 1986) presented a stability result that deals with the response of a nonlinear system to slowly varying input signals. In this work a proof is given, under a weaker hypothesis on the input signal, by constructing a Lyapunov function that is standard in the control literature. This proof may be more accessible than the other approaches. For completeness, brief proofs of some intermediate results that are regarded as well known are included. A simple example is given to show that this approach can yield explicit bounds in certain situations of interest. >

[1]  Charles A. Desoer,et al.  Slowly varying system ẋ = A(t)x , 1969 .

[2]  H. Witsenhausen.  Separation of estimation and control for discrete time systems , 1971 .

[3]  K. Mani Chandy,et al.  Approximate Analysis of General Queuing Networks , 1975, IBM J. Res. Dev..

[4]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[5]  Frits C. Schoute.  Decentralized control in packet switched satellite communication , 1978 .

[6]  Simonetta Balsamo,et al.  An Extension of Norton's Theorem for Queueing Networks , 1982, IEEE Transactions on Software Engineering.

[7]  Pieter S. Kritzinger,et al.  A generalisation of Norton's theorem for multiclass queueing networks , 1982, Perform. Evaluation.

[8]  Aurel A. Lazar,et al.  Optimal flow control of a class of queueing networks in equilibrium , 1983 .

[9]  Zvi Rosberg.  Optimal decentralized control in a multiaccess channel with partial information , 1983 .

[10]  J. Walrand.  A NOTE ON NORTON'S THEOREM FOR QUEUING NETWORKS , 1983 .

[11]  Aurel A. Lazar,et al.  The throughput time delay function of an M/M/1 queue , 1983, IEEE Trans. Inf. Theory.

[12]  C. Reboulet,et al.  A new method for linearizing non-linear systems : the pseudolinearization† , 1984 .

[13]  M. Kelemen.  A stability property , 1986 .

[14]  Jie Huang,et al.  On a nonlinear multivariable servomechanism problem , 1990, Autom..

[15]  P. Kokotovic,et al.  On stability properties of nonlinear systems with slowly varying inputs , 1991 .