Jose B. Cruz, Jr. graduated summa cum laude with a B.S. in Electrical Engineering degree from UP in 1953. He went to the USA for graduate studies in that same field, obtaining his M.S. from the Massachusetts Institute of Technology and his Ph.D. from the University of Illinois at Urbana-Champaign.
Jose B. Cruz, Jr., or Joe to his friends, taught at the University of California at Irvine, the University of Illinois at Urbana-Champaign, and the Ohio State University. At Ohio State University he has been recognized as Distinguished Professor of Engineering (2004 to the present); Professor of Electrical and Computer Engineering (2004 to present; holder of the Howard D. Winbigler Chair in Engineering (1997-2004; Professor of Electrical Engineering (1992-2004), Dean of the College of Engineering (1992-1997); and Director of the Engineering Experiment Station (1992-1997).
With colleagues and students, Cruz developed several methods for the sensitivity analysis of dynamic systems with respect to parameter variations. These are useful for parameter tuning and optimization of systems, analysis of system degradation due to parameter drift and aging, and adaptive control and estimation. Together with a colleague, he established the concept of comparison sensitivity matrix relating system output errors without feedback to system output errors with feedback This comparison sensitivity matrix captures the effect of feedback on altering the influence of parameter variations on system output errors in multivariable feedback systems.
Also, with his students, he developed a methodology for obtaining multi-agent strategies for networked dynamic systems, wherein agents pursuing related but different objectives are in the same system that may have another team of multiple agents that is in a competitive or even in an adversarial situation. Complex business enterprises or military forces in a battle situation are some example categories of applications. They introduced Stackelberg strategies for dynamic games in 1972. Kyland and Prescott won the Nobel Prize in Economics in 2004 due to their paper in 1977, which demonstrated that the optimum strategies of dominant players are time-inconsistent. Time Inconsistency was mathematically proven earlier in their papers.