My main research interest concerns geometric methods in differential equations and control theory. I am working on local problems concerning the geometry of distributions, Pfaff equations and Pfaff systems. Many of these problems can be reduced to classification problems of nonlinear control systems. The techniques involved use results from singularity theory (singularities of functions and of vector fields) and from local symplectic and Poisson geometry. I am also interested in singularity theory of differential forms.
My earlier work concerns feedback linearization and feedback equivalence of control systems, realization theory, and Lie-algebraic techniques for discrete-time systems. I have also published two papers on random dynamics and evolution to fixed points for discrete systems. The most often quoted results are necessary and sufficient conditions for existence of realizations (SIAM J. Control 1980, and 1986) and a theorem stating that Frobenius integrability of certain distributions associated to a control system is equivalent to its feedback linearizability (Bull. Pol. Acad. Sci. 1980, common with W. Respondek).
Critical Hamiltonians and static feedback invariants in: Geometry of Feedback and Optimal Control, B. Jakubczyk, W. Respondek (eds.), Marcel Dekker 1998, pp. 219-256.
Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem, Ann. Polon. Math. 74 (2000), 117-132.
Local reduction theorems and invariants for singular contact structures (with M. Zhitomirskii), Ann. Inst. Fourier 52 (2001), 237-295.
Introduction to Geometric Nonlinear Control; Controllability and Lie Bracket - Lecture Notes of Summer School on Mathematical Control Theory, Trieste-Miramare, September 2001
Distributions of corank 1 and their characteristic vector fields (with M. Zhitomirskii)