The synthesis of stabilization control by output for certain class of continuous and pulse modulated undefined systems

Abstract

Consider the system x˙ 1 = ϕ1(·)+ρ1xl+1, . . . x˙m = ϕm(·)+ρmxn, x˙m+1 = ϕm+1(·)+u1, . . . x˙n = ϕn(·) + ul, where x1, . . . , xn is state of the system, u1, . . . , ul are controls, n l is not integer and l ≥ 2. It is supposed that only outputs x1, . . . , xl are measurable (l < n), ϕi(·) are non-anticipating arbitrary functionals, 0 < ρ− ≤ ρi(t, x1, . . . , xl) ≤ ρ+. With the help of backstepping method, we construct the square Lyapunov function and stabilize control for global exponential stability of closed loop system. The stabilization with the help of modulators with sufficiently elevated frequency of impulsation is also considered.