in this paper the active vibration control of a four-story shear frame instrumented with piezoelectric actuators is presented. the piezoelectric actuators are hosted on the columns in two manners and the produced controlling forces by actuators are considered in the equation of motion. the smart structure modeling and control design is carried out using matlab software in state space form. subs...

We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions of these results. Finally, we obtain the first nontrivial upper bounds for the fundamental problem of the maximal size of independent systems. These bounds d...

Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximal complementary solutions. Maximal complementary solutions can be characterized by optimal (tri)partitions. On the other hand, the solutions provided by simplex{based pivot algorithms are given in terms of complementary bases. A basis identi cation algorithm is a...

We consider the stability of the feedback connection of a strictly proper linear time invariant (LTI) stable system with a static nonlinearity expressed by a convex quadratic program (QP). From the Karush-KuhnTucker (KKT) conditions for the QP, we establish quadratic constraints that may be used with a quadratic Lyapunov function to construct a stability criterion via the S-procedure. The appro...