The characteristic equation of the control system is s5+15s4+85s3+225s2+274s+120=0 . What are the number of roots of the equation which lie to the left of the line s+1 = 0?

State Variable Analysis and Design topics include: Concepts of state, state variables and state model, solutions of state equations, controllability and observability, pole placement by state feedback, observer systems and state models for linear continuous-time systems. State-variable analysis, also known as state-space analysis, is a procedure that can be used to analyze and design systems. It can be applied to linear and nonlinear circuits, as well as circuits with time-varying parameters.  A state variable is a characteristic of a system that can be described by a set of first-order... Show more

State Variable Analysis and Design topics include: Concepts of state, state variables and state model, solutions of state equations, controllability and observability, pole placement by state feedback, observer systems and state models for linear continuous-time systems.

State-variable analysis, also known as state-space analysis, is a procedure that can be used to analyze and design systems. It can be applied to linear and nonlinear circuits, as well as circuits with time-varying parameters. 

A state variable is a characteristic of a system that can be described by a set of first-order differential or difference equations. The state variables are the variables needed to describe the system's behavior. The number of state variables represents the order of the system. 

The elements of state variable analysis include:
State vector
State space
State equations
State variable representation 

The state variables for a given system are not unique. The state variables must be linearly independent and a minimum number of them must be chosen. 
In electrical networks, the state variables might be capacitor voltage and inductor current.

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