This paper deals with an efficient algorithm for dampers’ viscosity optimization in mechanical systems. Our algorithm optimizes the trace of the solution of the corresponding Lyapunov equation using an iterative method which calculates a low rank Cholesky factor for the solution of the corresponding Lyapunov equation. We have shown that the new algorithm calculates the trace in O(m) flops per i...

We study the stability properties of a class of time-varying nonlinear systems. We assume that nonstrict input-to-state stable (ISS) Lyapunov functions for our systems are given. We posit a mild nondegeneracy condition on our given Lyapunov functions under which strict ISS Lyapunov functions for our systems are also known to exist. However, the known existence result is based on value function ...

The problem of pth mean exponential stability and stabilizability of a class of stochastic nonlinear and bilinear hybrid systems with unstable and stable subsystems is considered. Sufficient conditions for the pth mean exponential stability and stabilizability under a feedback control and stabilizing switching rules are derived. A method for the construction of stabilizing switching rules based...

Input-to-state stability (ISS) of a feedback interconnection of two discrete-time ISS systems satisfying an appropriate small gain condition is investigated via the Lyapunov method. In particular, an ISS Lyapunov function for the overall system is constructed from the ISS Lyapunov functions of the two subsystems. We consider parameterized families of discretetime systems that naturally arise wh...

This paper studies the control synthesis problem of Takagi–Sugeno (T–S) fuzzy systems. By splitting the premise variable spaces and using the properties of fuzzy sets, a new control scheme is proposed based on a new class of fuzzy Lyapunov functions, and a convex condition for designing fuzzy controllers is given, where the new fuzzy Lyapunov functions and fuzzy controllers are constructed base...

We present a fast, simple matrix method of computing the unique invariant measure and associated Lyapunov exponents of a nonlinear iterated function system. Analytic bounds for the error in our approximate invariant measure (in terms of the Hutchinson metric) are provided, while convergence of the Lyapunov exponent estimates to the true value is assured. As a special case, we are able to rigoro...

Swarm principles are increasingly being used to design controllers for the coordination of multi-robot systems or, in general, multi-agent systems. This paper proposes a two-dimensional Lagrangian swarm model that enables the planar agents, modeled as point masses, to swarm whilst effectively avoiding each other and obstacles in the environment. A novel method, based on an extended Lyapunov app...