Analysis and Synthesis of State-Feedback Controllers With Timing Jitter

• Published in: IEEE transactions on automatic control Vol. 54; no. 3; pp. 652 - 657
• Main Authors: Skaf, J., Boyd, S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Clocks; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Controllers; Degradation; Equations; Exact sciences and technology; Linear matrix inequalities; Linear matrix inequality (LMI); Linear systems; Lyapunov functions; Lyapunov method; Mathematical models; Performance degradation; Sampling methods; Synthesis; Timing jitter; Performance evaluation; Lower bound; State feedback; Sampled system; timing jitter; Jitter; Feedback regulation; Continuous time; Linear time; Linear control; Convex programming; Closed feedback; Upper bound; Heuristic method; Linear matrix inequality; Timing; Linear matrix inequality (LMI); Lyapunov function
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2008.2010998

We consider a continuous-time linear system with sampled constant linear state-feedback control and a convex quadratic performance measure. The sample times, however, are subject to variation within some known interval. We use linear matrix inequality (LMI) methods to derive a Lyapunov function that establishes an upper bound on performance degradation due to the timing jitter. The same Lyapunov function can be used in a heuristic for finding a bad timing jitter sequence, which gives a lower bound on the possible performance degradation. Numerical experiments show that these two bounds are often close, which means that our bound is tight. We show how LMI methods can be used to synthesize a constant state-feedback controller that minimizes the performance bound, for a given level of timing jitter.