Abstract
In this article we present an ordinary differential equation based technique to study the quadratic stability of non-linear dynamical systems. The non-linear dynamical systems are modeled with norm bounded linear differential inclusions. The proposed methodology reformulate non-linear differential inclusion to an equivalent non-linear system. Lyapunov function demonstrate the existence of a symmetric positive definite matrix to analyze the stability of non-linear dynamical systems. The proposed method allows us to construct a system of ordinary differential equations to localize the spectrum of perturbed system which guarantees the stability of non-linear dynamical system.
Highlights
The stability analysis of dynamical systems and its applications to control theory have attracted many researchers [1,2,3,4,5,6,7,8]
The contribution to some classical problems in Lyapunov stability, LQ control and controllability has given in eguation [2] by exploring theorems of alternative for linear time invariant systems and the determination of qualitative properties for the possible solutions corresponding to linear time invariant systems
The non-linear differential inclusion is a strategy which uses the system model to control it and removes the gain scheduling and improves the performance of the non-linear systems under consideration
Summary
The stability analysis of dynamical systems and its applications to control theory have attracted many researchers [1,2,3,4,5,6,7,8]. A various number of problems appearing in systems and control are reduceable to standard convex and quasi convex problems involving linear matrix inequalities [20]. These linear matrix inequalities problems possesses analytical solution up to a few special cases but such problems are solveable with existing numerical techniques. These inequalities appears in the form of Lyapunov or algebraic Riccati inequalities which signify the computational cost of control theory based on the top of solutions of algebraic Riccati equations to a theory based on the solution of Lyapunov inequalities.
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